You might be thinking of the Ostrogoths and the first Kingdom of Italy. The Lombards are the gold standard of not having their shit together, but not all of it was their fault.

Although the Ostrogoths had been given lands in Pannonia in exchange for the defense of the upper Danube, the eastern emperor Zeno came to the conclusion that the Ostrogoths were more trouble than they were worth (fighting with him, fighting with each other, and in a general sense just being another nuisance to deal with) so he convinced their King Theodoric to go conquer Italy. This way, they would stop annoying him, and he could also get rid of Odoacer, another potential opponent.

Who was Odoacer? Flavius Odoacer, the de facto leader of the Foederati or ethnic "Barbarians" fighting for Rome (who by now made up most of the army) had deposed Romulus Augustulus when the emperor lost the majority of the army's favor (this was no cakewalk. Odoacer had to fight several pitched battles against armies commanded by Romulus' father and uncle). After coming to power, Odoacer openly admitted that although he might rule Italy, he was powerless beyond the alps, and consequentially didn't call himself Emperor. Instead, he sent the imperial paraphernalia to Constantinople and asked to be recognized as "Consul". Odoacer kept all of the functions of the Roman Administration in Italy intact, although there was a big political upheaval, there wasn't much of a cultural upheaval (Flavius Odoacer himself was so romanized historians aren't sure which "Barbarian" ethnic group he belonged to).

Odoacer initially played lip service to the previous emperor Julius Nepos (whom Romulus' father had deposed), even minting coinage in his name, but may have been involved in the plot whereby he was murdered. Regardless, after the murder of Julius Nepos, Odoacer asked to be given the title of Patrician by the Eastern Emperor, and be recognized as the ruler of Italy under the wing of a single Roman Emperor in Costantinople.

When Zeno sent Theodoric on his mission, he could afford to lose Theodoric's army as the bulk of soldiers in the eastern empire were still "Romans", as the large recruiting grounds of Anatolia and Armenia were not yet subject do destabilization (using the word "Romans" as they themselves would have: to denote citizens of the empire).

Theodoric the Amal, King of the Ostrogoths, had been raised in Constantinople. His had lived within the Eastern Empire's borders for centuries. When Theodoric defeated Odoacer and set up the first Kingdom of Italy, he did his utmost to further maintain the Roman institutions, law, and judicial system. However, he did not rule from Rome, rather, he ruled from Ravenna, seaside city conveniently defended by swampy surroundings, and easily supplied by ship.

So here we are, soon after the "Fall" of Rome, the first Kingdom of Italy was established as a client state of Costantinople. Including Odoacer's rule, we can say that the First Kingdom of Italy lasted between 476 and 553 as a political entity no less stable (if not slightly more stable) than the late Roman Empire. Why did this kingdom end? Justinian decided to reconquer Italy. And he did.

However, under Justinian we start to see signs of the Byzantine Empire's chronic manpower problem, and consequentially lost Italy in less than a generation. Although Justinian was definitely a great wartime politician (who was particularly good at picking the right man for the right job), his conquests stretched Byzantium's resources too far, and even sympathetic chronicles criticize him for being unable to defend what he conquered.

Thus, the sparsely defended Italian lands were easy prey for one of the last great "Barbarian" migrations: that of the Lombards. The Lombards would contest Italy nearly continuously with the Byzantines from the 6th to the 8th centuries. The Lombards moved into the Northern Italian Plains with relative ease, while the Byzantines would hold onto the Pentapolis (the five cities along the eastern coast of Italy near the mouth of the River Po defended by swamps and easily supplied by the sea), the city of Rome and its surroundings, and the easily-reachable Calabria and Puglia regions of Southern Italy.

Between founding the second Kingdom of Italy in 568 and Charlemagne's conquest nearly two hundred years later in 774, the story of the Kingdom of Italy was one of near-continuous warfare with the Eastern Empire. The Lombards "Went Native" very rapidly imitating the Roman Imperial customs, establishing Mediolanum (modern Milan) as their capital. They subdivided Italy into various feudal subdivisions. Had things gone differently, perhaps Italy would have survived as a medieval state, and centralized as the rest of Europe did over the course of the renaissance. As those bizarre historical turns of events would have it, the Kingdom of Italy would again be dismantled just when the Lombard King Desiderious (d. 786) got very close to finally kicking the Byzantines out of Italy. A successful offensive saw the encirclement of the Pentapolis (that to this day are called "Romagna" since the Byzantines were the last "Romans" to leave) which allowed Desiderious to march south against Rome unopposed. With the Byzantine army cornered in the Pentapolis and fearing a loss of independence for the bishop of Rome, who had been pretty much guaranteed a free hand to rule the "Duchy of Rome" (modern Lazio) in exchange for nominal Byzantine rule and military access, Pope Adrian cried "Uncle", excommunicated Desiderius, and asked Charlemagne to come to his aid. Charlemagne, even though he was busy conquering what would later become Germany, was immediately flattered and marched for Italy.

Charlemagne marched down from Germany in two columns, one under his personal command taking a westerly route, through the Valley of Susa, and another under his uncle, Bernard, through the Valley of Aosta. An ancient system of walls called the "Lombard Locks" (Chiuse Lombarde) sealed off the valley of Susa, and defenses personally commanded by King Desiderius held fast against Charlemagne's assault. However, the Valley of Aosta was guarded by Desiderius' son, Adelchi, who had been entrusted with a much smaller force. Pushed back by the enemy at Ivrea, Adelchi was forced into a disorderly retreat. Desiderius withdrew to avoid encirclement, and barricaded himself in the ancient fortress of Pavia, while Adelchi withdrew all the way to Verona. Soon, Desiderius capitulated and would spend the rest of his days in a Belgian monastery; Charlemagne was crowned king of Italy, and Adelchi fled to Costantinople (which, in adherence to the principle, "The enemy of my enemy is my friend" saw the Byzantine emperor welcome the deposed prince now that Charlemagne was claiming the title "King of the Romans").

But Charlemagne, although crowned "King of Italy" had gone no farther south than Rome; he still had to subjugate the other half of the Italian peninsula. Or did he? Seeing Charlemagne and his army at the gates of Salerno, Duke Arechi of Benevento, a powerful and fiercely loyal vassal of the deposed King of Italy (he had married Desiderius' daughter) came to an agreement with Charlemagne. Sending his son Grimolado as a hostage to Charlemagne's court, he secured the right to continue ruling as Duke in southern Italy; and was even elevated to the rank of Prince.

On the death of his father, Grimolado was allowed to return to Benevento to claim the throne, on the condition that he mint coinage in the name of the Emperor, and demolish the fortifications that dotted Southern Italy. On his arrival, Grimolado immediately began strengthening the fortifications at Benevento and Salerno. Having made his intentions clear to the Carolingans, he then constructed a church dedicated to St. Sophia in Benevento; a direct challenge to the Byzantine empire, just in case they were harboring any thoughts of subjugating him. It looked like the Duchy of Benevento was independent and planning to stay that way.

The next hundred years would mark the ascent of the Principality of Benevento, and perhaps of Lombard culture as a whole; marked by the monuments constructed in Benevento would lead it to be called, "The Second Pavia" (which had been the capital of the previous Kingdom of Italy), and the great wealth of the city of Salerno, which became major mediterranean entrepôt, and become home to a renowned school of Medicine. Successive aggressions, both by Charlemagne's successor Ludovic and his vassals in Italy were successfully repealed, either by force of arms or diplomacy. However, instability would be a hallmark of the principality; as successive invasions by the Byzantine Empire would again reclaim the regions of Calabria and Puglia, while dynastic infighting would split the kingdom three ways by the mid 9th century; the Duchy of Benevento, the Duchy of Salerno, and the Republic of Amalfi (ironically, each capital is within an hour's drive of each other, although the individual territories stretched far in different directions).

Edit: Holy shit, there are a ton of inconsistencies caused by copy-pasting. I've done my best to fix these.