Zap your PRAM by holding down Command(apple key), option, p, r keys while booting. The system will do the startup chime again if successful. Continue to hold down those keys until your system chimes 2 more times. This clears the parameter ram which holds settings for control panels among other things.
Rebuild your desktop by holding down Command (apple key) and option before your hard drive icon appears on the desktop on bootup. It will ask you if your want to rebuild the desktop. Tell it yes for this and every other drive it asks about.
If this does not clear your problem immediately, try booting off the System CD-ROM by holding down C while restarting with the System CD-ROM in the drive. If you can access floppies fine from this boot, then reinstall your system. If the problem is still gone, add back your third party extensions slowly to see if one is causing a problem.
If you still have problems after all this, I would say you have a hardware issue of some sort.