i'm guessing that you are using Windows 95/98, since newer Windows versions do not have these blue screens. i've used 98 before, and it is not too stable compared to Win2k and WinXP.
possible problems:
1. it could be a software conflict with another game, from a different company. trying uninstalling your other games one by one, and rerun Geneforge until the blue screens stop, which means you have uninstalled the game which caused the conflict.
2. not enough RAM. Win98 uses your hard drive for RAM equivalents when there is not enough memory at the moment, making your system very slow and unstable, hence the blue screen and Geneforge crashing on you. the solution here is to buy an extra chip.
3. some vital files in Geneforge could have been corrupted when you typed in the registration code. try uninstalling, then reinstalling the game.