Well, whether the static thing is new or old, look for all the same things I listed.

You still haven't answered about how the amp and player are wired up.

And when you say "the LED glows", do you mean that it pulses slowly bright to dim? If so, then it's correctly going into standby.

If that causes a thump WITH THE RCA CABLES DISCONNECTED AT THE AMPLIFIER END then you're very likely looking at a faulty amp.

Unless there's something screwy with the wiring.