You'd have to ask Caesar that. What exactly Caesar personally wanted out of the Parthian campaign has been a subject of speculation since antiquity. The campaign was certainly publicly cast as a response to Crassus' bumbling campaign at Carrhae, but the explanations that different sources give for Caesar's personal motive are all different. Suetonius, Appian, and Plutarch all give reasons for Caesar's interest in a campaign against the Parthians. Suetonius says simply that Caesar intended a campaign first against the Dacians and then against the Parthians, intending to invade through Armenia and test the Parthians there in battle before advancing into Media and the Mesopotamian plain (rather than rushing headlong towards Ctesiphon like Antony would a few years later). Suetonius doesn't directly provide a reason for this, but he includes the Parthian expedition in the list of works and deeds that Caesar planned "de ornanda instruendaque urbe, item de tuendo ampliandoque imperio" ("regarding the adornment and furnishing of the city, and also the holding and increasing of the empire"). Gelzer offered as a reason that Caesar was frustrated with the bullshit of Roman politics, where his enemies were still trying to foil his ambitions despite the fact that he demonstrably held all the cards, and intended to go off to Parthia to get rid of himself of their presence. That's more or less what Appian says, that Caesar planned a campaign against the Getae and the Parthians to escape the plot that Appian thinks he knew was coming and because he was tired and fed up with his failures at Rome, particularly his failure to get the people to accept him as king at the Lupercalia. Appian also mentions that perhaps he was sick as well. I find Appian's explanation very hard to believe. For one thing, it's not at all convincing to suppose that Caesar knew there was a plot, and no other source suggests anything but surprise on Caesar's part when the murderers attacked him. It's possible that an earlier plot in 45 under Gaius Trebonius might have been known to Caesar when Antony rejected Trebonius' offer to join in, but even that's unlikely as Trebonius continued to enjoy Caesar's favor in 45 and 44, being appointed suffect consul in 45 and awarded the proconsulship of Asia for 43. It's even less likely that Caesar knew about the Brutus/Cassius plot, which was a jealously-guarded secret (even if many, like Cicero, knew that something was up). Even harder to swallow is the idea that Caesar was frustrated by his failures. What failures? The only action that Caesar had failed in was his attempt to get himself made king, in everything else he had succeeded. But Appian assumes that the affair at the Lupercalia was Caesar's idea, which is not at all clear from the other sources. Plutarch says that Antony rushed up to Caesar during the Lupercalia and placed the crown over Caesar's head, and that Caesar rejected it. Plutarch thinks this was some sort of test on Caesar's part to see the mood of the people, but Suetonius very much disagrees. Suetonius specifically says that Caesar could not rid himself of the reputation that he wanted to be king, despite several times protesting it. Suetonius says that the first occasion was during a festival when a supporter of Caesar's placed a laurel wreath with a royal fillet on one of his statues: Caesar, according to Suetonius, made the mistake of scolding the tribunes of the plebs when they tried to arrest the man who did it, saying that he was insulted that they had not given him the chance to reject the honor of kingship personally. Suetonius says that when the people hailed him as king he responded that he was not king but Caesar (Caesarem se, non regem esse responderit "he responded that he was Caesar, not king," with the pun--sadly lost in English--that Rex was not only the word for king but also a Roman name in and of itself. Caesar's response is then quite brilliant, since not only does he reject the title of king but his response makes it seem that he thought they got his name wrong--the implication is that Caesar is responding as though he can't possibly conceive of a situation in which the people might mean rex to be "king" and not the name Rex, and that therefore the very idea of kingship doesn't make sense to him). Suetonius places the affair at the Lupercalia squarely in the hands of Antony, he doesn't think of Caesar as having had any hand in it and seems to think that Caesar was rather surprised by it. And from what we know of how Caesar conceived of the civil war and his ascension to the dictatorship I don't think that Appian has a leg to stand on when he says that Caesar's ultimate goal was so certainly to become king that the failure at the Lupercalia alone was grounds to abandon Roman politics. I prefer Plutarch's explanation:

ἐπεὶ δὲ τὸ φύσει μεγαλουργὸν αὑτοῦ καὶ φιλότιμον αἱ πολλαὶ κατορθώσεις οὐ πρὸς ἀπόλαυσιν ἔτρεπον Τῶν πεπονημένων, ἀλλ᾽ ὑπέκκαυμα καὶ θάρσος οὖσαι πρὸς τὰ μέλλοντα μειζόνων ἐνέτικτον ἐπινοίας πραγμάτων καὶ καινῆς ἔρωτα δόξης ὡς ἀποκεχρημένῳ τῇ παρούσῃ, τὸ μὲν πάθος οὐδὲν ἦν ἕτερον ἢ ζῆλος αὑτοῦ καθάπερ ἄλλου καὶ φιλονεικία τις ὑπὲρ Τῶν μελλόντων πρὸς τὰ πεπραγμένα

But his many successes did not turn his ambitious [literally "doing great things"] and honor-loving nature to the enjoyment of what he had already worked at, but these successes being the fuel and incitement for future deeds they produced in him thoughts of greater plans and a love of fresh glory, as though what he had done was exhausted, and indeed that feeling was nothing other than rivalry against himself, just as against another, and the rivalry [literally "love of conflict"] between what he had done and what he intended to do

This, I think, fits what we know of Caesar's personality much more than any of the other explanations we get. Certainly Caesar proposed to avenge Crassus and all that, and probably meant it. But ultimately we see in Plutarch's explanation the explanation for just about everything that Caesar did: his own dignitas. From what we know about him Caesar seems to have been obsessed with always winning greater honor for his reputation, always increasing his dignitas, either through war or the consulship or the magnificence of his consular and dictatorial legislation. Caesar thrived on rivalry, always trying to outdo somebody to become the greatest--hence Lucan's line in the Pharsalia:

Nec quemquam iam ferre potest Caesarve priorem/Pompeiusve parem

Neither could Caesar bear anyone greater than he, nor Pompey any equal

And we do see, and the ancient scholars and contemporaries of Caesar generally agreed, that Caesar was always trying to fight to be the top, to be the guy that was always first in everybody's minds. The man was of tireless energy--Plutarch says he would work through the night and sleep in his carriage so he didn't have to stop working, and he wrote poems and speeches for fun, including an epic poem called the Iter written in 24 days during his journey to Munda! It's easy to believe that, as Plutarch says, he became restless doing nothing but being in charge, and it's equally easy to believe that Caesar's almost pathological need for rivalry made him seek out rivals to beat--how better to prove he really was the greatest than to knock out the people who had defeated his own rival Crassus and who now stood proud and unbowed? Not that the man liked fighting or anything. But one way or another we can't actually know, since we have no statement from Caesar about his personal motivations.

As to how much power Caesar personally had...it was a lot. In 44 Caesar commanded 14 legions, having disbanded about half of his legions the year before. With his dictatorial powers, however, he maintained the right and power to recruit more at will--if the 60-some-odd legions that Octavian had after he won Actium are any indication, the full muster of Roman manpower that could've been thrown at the Parthians was pretty mindblowing. Apart from Caesar's personal fortune (which itself was more or less limitless--by 44 he was undeniably the wealthiest man in Roman history up until that point) he could call upon the tribute of the provinces and all the revenue of the state if he felt he needed it, although in practice it's doubtful whether he actually would've ever done so. And the name of Caesar alone was worth something. Caesar was mystifying, he had this "demonic charm," as one scholar put it, that drew people in and terrified those who opposed him. When Antony refused to grant Octavian access to Caesar's fortune according to the conditions of his will, Octavian capitalized not only on Antony's rather touchy reputation among many of the Caesarians but also on the fact that he bore Caesar's magical name--that fact alone was enough to attract many Caesarians who sided with Octavian early on.