G3 is very very old server, most are retired now. 99%\
12 years old servers...
it is so old it has floppy drive ! yes that old. and PCI slots no express slots old. (relic it is)
Does it have the 2 CPU option:?
did you read the server logs? it has logs!
it records all shut down causes on my bigger/newer G7
It will shut down by self for a 3 reasons.
it overheats, or the PSU is bad. or the PSU was overloaded.
mine even has power log, that proves that and 2 PSU's that auto backup power, if one is bad. of the 2. (you have only 1 PSU on this old server ,unlike my G7)
is this your only 330? no spares ? as most servers installations have (all do really for clustering)
clean out the dust in the CPU heat sinks and make sure all fans work first? that be first. so it cant overheat
did you first change out the COIN cell on the MOBO,
bottom of motherboard see that Cell it be NO GOOD at 12years
old ever. and makes the BIOS go Nuts and RTC clock same.
no logs, ever heard of iLo (lights out)
its built in micro web page. and its own IP address
you connect to it and read the shut down logs.
data sheet it is at HP, as is full help at HP real. HPE its called
on mine I can see 6 fan speeds
and 21 temperature readings at any time.
under system information page in iL0
and then the iLo event log. mine says admin turned it off last night.(a video server it is , here)
but read the logs first.
this be the first place to look on any HP Prolaint ever made.