Windows 7 if a 64 bit OS and it can recognize more than 4GBs of RAM.
I would suggest anyone with Windows 7 that intends to do serious gaming get at least 2x 4GBs. RAM is really cheap so there isn't a good reason not to fit more than 4 GBs in a Windows 7 computer.
As for the other question, I wouldn't upgrade anything except maybe a video card in the DELL.
Save your money for an entirely new core. Cores are best upgraded as one "piece" so a Motherboard, Processor, and RAM should all come at once.
You can get a Phenom 2 x4 840, M4N68T-M LE V2, and 2x 2GB Crucial Ballistix core for well under $100 if you are thinking of just upgrading the whole core and you are on a budget.