If the RTC battery fails the normal failure mode is back to Jan 1, 1980 or thereabouts and you get an error message saying setup is bad. Once you go to setup and change things, then the machine should be good until you power cycle (off for a minute then back on) the machine.
Once power is established and not removed you should be able to do a hot boot or restart without the RTC battery being involved at all.
If it fails on the hot boot then I would suspect memory problems. Try reseating the memory.
If it is a RTC problem it is not worth the effort. The battery may be changeable. If the battery looks like a nickle, then you can buy replacement at Office Depot. Get the right size. I have changed the clocks, the clock crystals, and the soldered in batteries, but I have the parts and tools and I won't do it anymore except the battery.
Your Partition Magic problem shouldn't be related. What operating system are you using and can you boot into it from a floppy?