"For some reason the great powers all want territory and influence there, but at the same time they prevent anyone from taking power there and if by any chance a native Balkan nation starts rising in power, they do everything in their power to suppress it and neuter it."

That sounds like a very succinct summary of "The Eastern Question" and the balance of power that European powers sought to maintain there.

What was at issue with the Eastern Question in the late 19th century and early 20th century was the fate of the Ottoman Empire. It's worth remembering that even after the independence of Serbia, Bulgaria and Romania, the European part of the Ottoman Empire was a fairly substantial chunk of the empire as a whole. It was maybe something like at least 4 million of the empire's 20 million inhabitants around 1905. The area had a major city - Salonika, and was the home of such political movements as the Young Turks, the Ottoman Third Army, and was even the birthplace of Mustafa Kemal, future Ataturk.

While it's true that much of the Balkans is mountainous and doesn't have major resources, there are exceptions, as lowland areas, especially in Thrace and around the Danube, were very fertile agricultural regions. But perhaps the most important aspect of the area from European powers' perspectives was its strategic location: the region controlled the delta and southern bank of the Danube, and controlled access to the Bosphorus and Black Sea. The area also saw a fair amount of railroad construction in the late 19th century, especially of the famed Orient Express linking Istanbul and Vienna. A lot of outside interest in the region was less for what the region contained and more for where it was, and what it lay in between.

To start with Russia: Constantinople was most definitely the prize. Not only would control of "Tsargrad" greatly elevate the Russian tsar's pretentions to being inheritors of the Byzantines, but control of the Bosphorus meant a prized warm-water port for the Russians, and control of access to and from the Black Sea, which was essential for wheat exports from Ukraine. Control of the Balkans was part of the strategy getting there, and this was encouraged both by Russian pretensions to protect Eastern Orthodox Christians (which conveniently described Romanians, Serbs, Bulgarians and Greeks, to name a few), but also played into late 19th century Russian ideas of Pan-Slavism, ie that the Russian state could unite all Slavs under one rule. So Russia in particular had very strong ideological and strategic regions for increased control of the Balkans, whether through direct annexation or setting up client states (like the 1878 San Stefano version of Bulgaria was to be).

The number two great power interested in the Balkans was Austria-Hungary. Austria-Hungary's interest in the region came from a number of causes. First, it was an area of territorial and military expansion that could partially offset the stinging losses of major territory in northern Italy that had been lost in the Italian wars of unification (such as Milan and Venice). Second, it was an area of almost semi-colonial influence - Austria-Hungary was able to either militarily occupy parts of the Balkans, like Bosnia-Herzegovina, or exert a major sphere of influence over other parts, such as Serbia. The latter was begun with the Austro-Serbian Treaty of 1881, which saw Serbia become something of a satellite state of Austria-Hungary, with the latter assuming major economic influence. Much of Serbian exports, such as pork, went to Austrian markets (and become subject to punitive tariffs in the 1906 "Pig War"), for example. Third, Austrian influence in the region was seen as a check for internal political reasons and external strategic reasons. The external strategy was clear - limit Russian influence so close to Austria-Hungary's borders. The internal concerns were delicate - with the rise of nationalism among Austria-Hungary's minority populations, there was a hope to keep the region under Austrian influence and free of strong local states that could inspire or foment separatist nationalism within Austria-Hungary proper. Serbia was a major concern here.

As for the other great powers, their interests in the region were largely tied to their concerns over Austrian and Russian power, and more general strategic and economic concerns. To this end, Germany, Britain and France were less concerned with territorial control of the Balkans per se, and more interested in influence (through economic control, through railroad construction, and through military advisors) on the Ottoman Empire as a whole. They tended to be the more moderating powers, trying to limit the encroachment of other Great Powers in the Balkans, or the control of too much of the region by any one local Balkan state.