My G5 iMac - a very early one - has recently started randomly powering off. Not shutting down, just switching off as if the plug had been pulled. It seems to happen more when the computer is heavily loaded.
Is this likely to be the power problem for which Apple has extended the warranty:
It's in the range of serial numbers listed.
"Consideration shall be given to the need for as many as 32 characters in some alphabets" - X3.4, 1963.