Download MemTest86, install it to a floppy diskette, leave it in your floppy drive and reboot, run ALL the tests (this could take well over 12 hours so leave it on over night if you can).
MemTest86 will detect errors in your memory, you can only be sure of this if you have run ALL the tests available. If it finds errors you then know that your memory is damaged and it needs replacing or returning.
Also something that does concerns me:
Specs:
P4 2.4Ghz (no oc)
Gigabyte GA-8SR533 no HT
333Mhz DDR 514MB NO-ECC
80GB Seagate
80GB Maxtor
128MB ATI Radeon 9800 Pro
Pioneer Dvd
Pioneer Dvd Writer(A106)
300 Watt
Audigy
1x80mm Fan
Is the fact that your running a 300Watt PowerSupply, this is NOT enough power for your system..
Your running a very power hungry system, 2 Hard Drives, 2 Optical Drives, a SoundBlaster Audigy, Pentium 4 2.4GHZ not only that.. but a ATI 9800Pro 
Running a Pentium 4 2.4GHZ / 2 Hard Drives / 2 Optical Drives / 1 Peice of Ram, would be pushing the powersupply as it is.. let alone running an Audigy SoundCard and a ATI 9800Pro (2 VERY demanding components).
Basically your powersupply is not about the “Wattage” (300W / 400W) all it means is that your powersuppy can outpu a Maximum of “300W”, powersupplies have different “V Rails” (Voltage Rails):
+3.3V +5V +12V -5V -12V and these are calculated by the “Amps” the powersupply can supply to these “Rails”
On a good 300W powersupply you would still be pushing to provide enough power on your Voltage Rails to have a stable system.. if you can in your bios you should be able to check the Voltages that are being supplied to the different V Rails for example:
+5V is showing up in your BIOS as: “4.35V” then that is TOO low, your powersupply should be providing enough power to supply your Voltage Rails with slightly more than was is required, in my pc: my +5 is +5.11V (example)
Run the MemTest, if you do get errors, you will need to replace your memory, and you will need to get a new powersupply as this is most likely the cause of your troubles.