I've seen office politics like this on several occasions and it can be very painful. It's natural for folks to want control, credit, and autonomy, but not blame if something goes wrong.
The 7 Habits book has great advice on this topic and says it more eloquently than I can.
Suggestion 1: Proactively cooperate with the other department
Maybe they're not too interested, but it would still be good for them to be in the loop. You could share the occasional status report with your recent accomplishments and next steps. You could invite them (maybe as optional) to a demo. If you feel you need input from them before you can proceed, politely ask for it. As far as credit is concerned, I've had more success shunning credit and thanking others than trying to "strategically" win credit. It's obvious to smart people who the real contributors are.
Suggestion 2: Proactively tackle the challenges and deliver the solution iteratively
If you or your team has the bandwidth and know-how to take on the challenges - go for it! Politely and with consideration for your team, other teams, and the company - present solutions. It's ok for a solution to be not-totally-perfect on the first iteration because feedback is so valuable and helps ensure you're on the right track. Again, be careful to avoid gloating or seeking credit because this tends to attract hostile feelings. Be generous and positive - never whiny.
"But we really can't make progress without this other team!" If this is the case, maybe it best that another team own it - you could propose this. Maybe you can own it if you just get a little advice on how you might proceed.
"But my boss wouldn't want me to take such risky ownership" I've seen this case too often. Risk taking and iterations are necessary. Be careful to present awesome solutions but without wasting (or being perceived as wasting) a ton of company resources. I once had to explain to my boss that I really really wanted to keep dabbling on this project even though he said, "don't work on it" and it paid off very well. Bosses are sometimes arrogant and misdirected and occasionally they have egos. Handle this with sensitivity.