Memory Vs GPU

Hello Everyone, i have a old system (see Attachment) that work great with 4 Gig of RAM, but with 2 Gigs it Randomly Freezes, (all updates are applied) it also has a On board ATI video (North Bridge: AMD 740) this was an ongoing issue untill i took the 4 Gigs out of my newer machine and put it in, i now think i have solved this on going issue, my question is, what would be the better purchase, a new Video card ? ( suggestions welcomed ) or 4 gigs of memory.
Thanks in advance.

Thanks for the Quick Reply, i am currently playing a few older game GOW, HALO, Tiger Woods,ect and they seem to be playing pretty well, the 4 Gigs will be going back into my newer machine, ( AMD 2 965 BE, EVGA 260, 750 PSU ) as soon as i decide on what to get, what kind of GPU would be recommended for a GA-MA74 Gigabyte MB, my current machine only has a 500 Watt PSU.

Thanks.

Thanks for the help, here is my problem, i have a fairly new build (see specs) and the PSU has died, i have another fairly new build also (built 6 months apart) AMD 2x240 GA-MA74GM-S
GIGABYTE - Motherboard - Socket AM2 - GA-MA74GM-S2 (rev. 2.0)

no card just on board Graphics, 500G HD and 4Gigs RAM, (taken from Spec machine), this machine is running very well, i would like to Either,

1, put the PSU from the second machine to see if the first machine can boot up.( currently it is not even posting,) even though i have had the motherboard tested and is working, and got a new CPU for it AMD2 Quad 965 ( and update W7) since that machine has not been used for over a year,
or
2, use the PSU in the first machine with just the on board video, untill i can get a PSU replacement for it,

I know that's not the best solution, but it would give me an idea to go from, at this time i cannot afford a new PSU , and to ship the one i have back to the manufacturer, i could buy another PSU for that price,

Thanks in advance,