Now, my first thoughts were a Radeon 7750. I am so confused on all the different ones that my mind feels it may explode.
I am told that power is the issue. I have no idea what my power is on this PC so this is my main question... Can it even run a 7750? if so... which is best for the price? I do want to get it as cheap as I can as money is tight.
You are right to be worried about the power supply, OEMs are notoriously tight when they spec them so I'd be surprised if it has 250 Watts available: not enough.
No harm in checking, though-take the side panel off, there will be a printed label on the PSU listing its outputs.
Although its not a stellar performer, at least the system has a half decent CPU, and WoW can be hard on the processor, especially when things get busy.
If your brother is using the monitor that came with the system (19" 1440x900 resolution) a HD7750 will be a vast improvement over the built in graphics he's currently using and would be my choice as upgrade.
Be a good fellow and get a decent replacement power supply: Corsair, Antec, Silverstone and OCZ are names to trust.
Expect to pay £75 for a HD7750 and £40 or less for the power supply. If you stick to the names I have listed 400 Watts will be plenty, but do n't turn down a unit if it's cheap just because It has higher output.
This looks good, quality unit, good price: