Think it is impossible to flash the bios outside windows, so options are to try to reinstall windows, or mess with the bios settings to see if there is a way to flash it. Of course that is if it is a software problem and not hardware. If it is hardware there are a few utilities that can help diagnose the problem, good luck finding parts though. Best option for parts, is to call up dell and ask for their parts department. They can help find the correct parts for your computer, if they still have replacement parts that are compatible then you're in luck, otherwise, it isn't going to be easy to find them second hand.

Call dell up, ask for parts and give them your service tag and ask for a compatible motherboard, if they still have one on hand. Otherwise you're SoL. It will also be helpful to look up the part number and have that ready prior.