Name brand name computers tend to be "proprietary" which means "not easily upgradable".
The four big components to a system all have to fit together nice. The motherboard, RAM, vid card and processor. Change one and you'll probably need to change the rest.
I'd also suggest a new machine. You can keep your peripherals (keyboard, mouse, monitor, printer, etc) as they should be universal and just get a new tower.
Since we are both in the same neighborhood I can say that I had a very good experience with TG Officetex 3748 Harlem Rd (take the Harlem exit north off Genesee Rt.33 and its up there on the left about two lights next to the Kwik Fill.
Couldn't hurt to give them a call and tell them what you got and where you want to go. They will be glad to help you out.