Hmm, given your situation I suggest practicing some hardcore quid pro quo /favors for favors/ or whatever you want to call it.
I.e - get people to help you because they owe you one not because it's on their yearly goals or their manager told them to.
This means you need to do a bunch of nice things for various folks, with the risk some may not pay off. Who in other departments can you help? When someone does help you how can you turn the balance of favorhood back to you? e.g. if a bunch of people help you out on a high profile project maybe you lay on a lunch for them all - that way the favor is back in their court.
Develop personal relationships with folks in all kinds of departments and roles, even if they may not be in a position to help you in the immediate future you can build good will. Bob may never be in a position to help you directly, but might tell their buddy Sue how nice and helpful you are so that when you ask Sue for a favor she helps you out...
Depending how far you're willing to take it play up other types of relationship e.g. if there are some women co workers a good bit older than you maybe you can get them to be a bit motherly toward you and help you out on that basis - to avoid being sexist I will say you can take the same approach with men getting them to be fatherly. Even if the age gap is smaller you may be able to play on big brother/sister like relationships.
I'm hesitant to suggest flirting to get the help you need but if needs must and your moral compass allows it well that's up to you. Just think about the morals of that one and the potential for 'harmless' flirting to be misconstrued and lead to embarrassing/awkward situations or even accusations of sexual harassment.
I will now sit back and await the accusations of toying with peoples emotions, abusing relationships or even perhaps being Machiavellian.
Or perhaps, this is what my soon to be former boss meant when he said I had people skills - which I didn't really take as a compliment.
Then I'd take company funded classes in something I found interesting.
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