when led is on, check the voltage on stand by pin of amp IC.
If voltage is there, then this area of the circuit is OK.
But if mute voltage does not rise then there could be a fault at the amp chip.
Further more volume should not get warm as heavy current won't be flowing thru them but It might still work if it just stays warm and does not feel too hot.
Check other chips for warm up when led is on.
As for led turning on, there could be a solder jumpers or loose due to handling.
If voltage is there, then this area of the circuit is OK.
But if mute voltage does not rise then there could be a fault at the amp chip.
Further more volume should not get warm as heavy current won't be flowing thru them but It might still work if it just stays warm and does not feel too hot.
Check other chips for warm up when led is on.
As for led turning on, there could be a solder jumpers or loose due to handling.