OS X Bug? RAM Bug? How to test RAM?

My 3 year old iMac G5 is acting up again...
(2GHz - 1.5 GB DDR SDRAM)

I have had a constant sleep problem on it, since it was fresh out the box; it wakes up by itself.

Any suggestions to remedy this?
I tried to run it through a power back up, but that didnt make any difference..

Couple of days ago it went to sleep when i did, but when i came to it in the morning it was off; i started it and it gave me the 'OS had to shut down, bla, bla', press to see error report, that never shows up -box.
This is first time it happens to me.

In a case like this i would normally just re-install my OS, but last time i did so after getting a bug, it got really messed up (wouldnt install OS), so i ended up with sending it back to the store i bought it from and they found that the extra RAM they installed had a bug (pretty much a year after they put in my extra 1G RAM), so they changed it to a new - Now we are about one year on from that new 1G got installed, and i am getting problems again..

Is there a way to run a test on the RAM, or do i have to take it out?

Hope this helps you out:

Testing RAM

How To Test Ram Under Mac OS X

Quote:

Memtest is a Unix command-line program that does the memory testing, and is the Mac equivalent of MemTest86.