Computer Shutdown issues

[Phandalyon]

First off, Power supply has already been replaced with this one:

http://www.newegg.com/app/ViewProductDesc.asp?description=17-104-933&depa=0

I have an older PC that I have been running as a fileserver for a while now and recently it started random shutdowns on me. First instinct is, of course, Power Supply. So I picked up a new PSU and I am still having the shutdown issues. Anyone have any ideas? I have all the power saving features turned off becuase I use the computer as a pseudo HTPC.

Computer:
Abit KT7-A Motherboard
AMD Athlon 1000 CPU
512MB RAm (Corsair and Crucial Mixed PC133)
Fortron Source 300Watt PSU
Liteon DVD Drive
40GB Maxtor ATA133 HDD
120GB WDSE ATA100 8MB Cache HDD
Soud Blaster Live! Soud Card
Linksys LNE100TX NIC
ATI Radeon 7000 64MB Video
Maxtor external 160GB one touch backup drive - USB connection
Running Windows 2000 SP4 with all updates
Viruses and Spyware have been thoroughly searched for and cleaned.

CPU Temps tend to stay around the 33* mark. Cooling is provided by a Speeze Falconrock copper (80mm fan).

The computer is plugged into an APC Back-UPS 350 and only the PC and the external backup drive are plugged into the Battery. The backup reports on power outage in February, but does not have any other power issues listed.

I also have a wireless keyboard and mouse hooked up.

The shutdowns occur at random times and can sometimes take a few hours or a couple of days to occur. I hate random problems like this. Anyone have any ideas. I have been working on a couple of other issues on this computer (Related to network transfer and HD speed, not to power). I have everything else resolved now and I am getting great speed out of the computer, but this shutdown thing is still bothering me.

 

[HvyMtl]

first off - you have a 300 watt psu plugged into a 350va ups - (divided the va by half and you get the max watts the ups can handle... in this case 175 watts) you need to upgrade and this can cause funky issues...
do a memory test - that could be an issue - a stick of memory may have gone bad. do a hard drive test too.
double check all connects -
if the prob still exists - strip the system down to one hard drive, cpu, one stick of memory, vid card. and make sure those are seated well and if the prob persists try testing the parts in a known good system.
do a cmos clear
double check the power supply connects - make sure the motherboard is not grounding on the case.
look the motherboard over hard (as older abits like this do fail more often than they should - brother has gone thru 3 of those) check the capacitors for any bursting/leaking.
try those and good luck