Sounds like you're probably having hard disk problems. Were I you, I'd back up the drive and run full diagnostics on it before trying to reload any software. At the very least, I'd do a low-level format (if possible). Then I'd put System 7.5.5 or 7.6.1 on it.

I'm pretty sure those things had trickle power that sustained the PRAM settings in addition to the battery. As long as it isn't unplugged, it should keep its date/time settings. Otherwise, a new battery is only about $10 at Radio Shack, and a good buy for a machine that sees regular use.