Without any POST beeps/messages, and with all extra hardware removed (eg. GPU, etc.), it could be any of the 3 main components (motherboard, CPU, RAM) at fault. Process of elimination is the only thing that works here.
What do you have on hand (or can borrow/obtain cheaply) in terms of:
- Additional sticks of DDR3 RAM?
- Additional AM3/AM3+ motherboards?
- Additional AM3/AM3+ CPUs?
They don't have to be expensive hardware so long as they're compatible with what you're testing.
As SSG Salvatore suggested, trying your current RAM in another motherboard and/or other DDR3 RAM in your current motherboard could help you find some sticks of RAM that you know work (to be used for subsequent tests).
There could be faulty CPU contact with the motherboard. Try re-seating it (have some thermal paste on hand). Re-try using the working RAM (per above). If that works, problem solved; but I'd keep an eye on it.
If that doesn't work, you still won't know if it's the motherboard or CPU. For that, you'll need to slot the CPU in a different (working) motherboard along with RAM you know works (per above). If it boots up, then you're probably dealing with a faulty motherboard. If it fails to boot, then it's likely the CPU.
Hope that helps.
