Sounds like you have a bad power management unit (PMU). If the Powerbook is still under warranty, take it into an Apple Store/Repair shop. If not, try resetting the PMU yourself.
Sounds like your battery is close to dead. Do you have a TiBook or AluBook? I know the G3 PB and the TiBook there is an internal clock battery which if it dies loses time and can cause other problems like erratic performance. It could also be your main computer battery not holding a charge.
Sounds pretty bad. The time going back to a previous date (probably like 20 years ago eh?) usually means that the backup battery feeding power to the CMOS or BIOS chip.
Can you tell us more about the Powerbook, like what model and if it is plugged in and stuff.