His computer is an OLD dual CPU machine, not dual-core.... totally different decades. It's well past its prime.
Matt is on the right on with his suggestions. You won't need Pro, 4gb memory is fine, a quad-core may be over-kill for you, but will pretty much future-proof you for the life of the machine, and its pretty much standard hardware nowadays. If you ever need service, it'll most likely be an experience no matter what brand it is (think offshore support), but AFAIK Dell is still good about making things right for a machine still under warranty. HP, I haven't dealt with them in sometime, so I can't really say. Just remember, that most any computer bought today, most likely will NOT last as long as the one you currently have. It's the major down side to build it cheaper, cheaper, cheaper manufacturing.
If you were close by, I'd simply build one for you. In my 20+ years with computers, I've never bought a pre-built desktop.