ntoskrnl.exe Ram problem!

[TragedyPC]

My parents computer recently started having some very serious crashes. Time and time again it failed to boot even, luckily formatting and fresh installing the OS worked for a while (Thanks to me they have monthly backups, nothing was lost!) About a day and a half ago the crashes started again but this time with the RAM problem (Ntoskrnl.exe). Long story short, I need relatively cheap (and good for it's price) RAM. Around 30$'s or so.

 

System Specs:

Processor: AMD Athlon II X2 255 Processor 3.10Ghz

RAM: 4GB

System Type: 32-bit OS, x64 based processor

GPU: Nvidia GeForce 9200 (Yes I know it's awful. Walmart built)

I can also do an msinfo32 if necessary but I doubt any of this is.

 

P.S. I'm better off buying a new computer, but it's not in my best interest to do so right now.

[DebatED Nothing]

Looking online it seems this CPU supports DDR2 1066 and DDR3 1066, so would this work? http://www.amazon.co.uk/dp/B0038N2UZ4/?tag=pcp0f-2 it's in UK pricing but I think that's around about $30.