So you are saying your iPhone works at Starbucks, McDonalds, the university, in fact just about anywhere else but your house so the problem must be with the iPhone?
How long have you had this router? Did a little checking and there have been updates released by Belkin for their various 54g routers, most to fix bugs and to bring them into full compliance with the 802.11g and n specifications. This has been a problem all device makers have with updates, if they update the firmware on their device to be compliant then they may have a handshake problem with routers that are not in full compliance. There is no updates for your router due to the iPhone update.
I am assuming you have tried Forgetting This Network on your iPhone, doing a reset, and resetting the router then trying again. If not, give it a whirl. Also update the firmware on your router if necessary:
http://www.belkin.com/support/article/?lid=en&aid=5947
If none of these things work call AppleCare, give them the information regarding the router you have and the firmware level and information from your iPhone, other devices on the system, etc. and get a case number. If you do not do this there is no way for Apple's engineers to know their is some problem with Belkin routers in your scenario and no way for them to fix it. Every iPhone user I know is having no problems connecting their iPhone to various routers (I've connected to 4 different ones today) so this is not a system wide bug that is affecting all iPhones. So give them all the information you can to find a solution.