Summary:
Can I program a \"thick client\" game in C without reinventing wheels, or should I just bite the bullet and use some libr
Do you want to be able to play your game on a console? Do you want to do it as a learning experience? Do you want the final product to be cross platform? Which libraries have you looked into so far?
For a 2d game I don't think performance will be a problem, I recommend going with something that will get you results on screen in the shortest amount of time. If you have a lot of experience doing Python then pyGame is a good choice.
If you plan on doing some 3d games in the future, I would recommend taking a look at Ogre (http://www.ogre3d.org). It's a cross platform 3d graphics engine that abstracts away the graphics APIs. However for a 2d project it's probably overkill.