what motherboard is compatible with a Athlon 64X2 Dual-Core Processor 6000

Any AMD motherboard with a socket type of AM2 should be fine. But what other hardware do you have in your computer? What is your power supply? What RAM do you have?

Also, are you sure all you need is a new motherboard? Have you tested the other hardware in another computer? How did you diagnose the motherboard as the only problem? I ask because if it wasn't tested thoroughly, then you could end up replacing the motherboard and run into a cascading effect from there where you need to replace other parts as well.