You'll have a difficult time building a $500 gaming pc that includes a monitor.
but here's what I picked for you.
M5A97 or any M5 series Motherboards (AMD $40-80)
FX-4300 Quad Core 3.8Ghz CPU ($90-120)
Ripjaw 2x2gb (4gb) 1600 RAM ($55)
Some Cheap Mid ATX case ($40)
400-500W power supply ($55)
evo 212 cpu cooler ($30)
500GB HDD ($40)
That ranges from $350-420
leaving you $80-150 to buy any monitor of your choice
I didn't give any exact brands for some of them, because after all it's person preference for you. So get something around that price range.