Looking to buy a new PC... could use some advice?

[Bond]

So, it looks (actually sounds) as though my custom built PC all the way back from my days in middle school is about to explode, which means it's probably time to buy a new PC.

I'm looking for something in the $500-600 dollar range. Any suggestions as to if I should buy an HP or Dell (or another manufacturer)? Intel or AMD?

P.S. What is this dual vs. quad core business?