G4 suddenly shuts down, etc.

I recently purchased a G4 tower (Gigabit Ethernet dual 450MHz) for $50 (Craigslist). The previous owner stated that the computer would occasionally shut down or freeze with a kernel panic. Said he was told it was a RAM issue. I have been using it daily (a lot) for about 10 days and it hasn't given me much problem.

A few times it has been hard to start, sometimes I have to try starting it four or five times to get it to boot up, but once it boots it's usually fine. I haven't seen any kernel panics but I have had it shut down randomly a few times, but only after I've left it alone for a while. I was wondering if there are any hardware tests I can do, I'm still relatively new to Mac. It isn't terribly inconvenient, I am using the computer successfully now, but I would like to take care of it before I go upgrading and such.

Help is appreciated, Thanks!

Go to this link and download Apple Hardware Test for G4 Power Mac, version 1.2.6.

Apple Hardware Test Images

Drag the .dmg file to the left hand column of Disk Utility, pop a blank CD in to the drive and hit burn. Thagt will make a bootable copy of AHT. Pop CD into optical drive, reboot holding down 'C" and run the full test.

AHT will check the memory, logic board and other checks.