Though, buying a new computer does offer you the opportunity to throw the current one out the window, which could be very satisfying.
More seriously, whether I would buy a new computer would depend on how old and weak the hardware in the old one was. You say this is an HP Pavillion from 2002. That sounds old to me (but I'm a computer geek.) How much memory does it have, how big is the disk, and how fast is the processor?
Unless your answers to these questions suggest you got one of the biggest, baddest, fastest HP Pavillion's sold at that time, I would recommend doing what you seem inclined to do anyway - get a new computer. The increased performance will delight you.
I'd recommend checking out MonarchComputer.com's Value Desktop systems. Monarch is one of the top rated computer system vendors, according to my long time favorite rating site ResellerRatings.com.
I am here in Atlanta and can tell you Monarch rocks. I build my own, but I tell all that ask about them and another local builder.