My satellite receiver started to get very hot, I turned it off, and now it does not turn on.
I saw this when I opened. Please describe these spots.

 

Looks like the Large Black Capacitor on the PSU board ( bottom PCB, top picture) has leaked due to possible over voltage.

Can you take wider pictures of the psu board.

 

Has rainwater got into your tuner? Sometimes it happens when water gets inside the dish cable.
Good luck..

 

Has rainwater got into your tuner? Sometimes it happens when water gets inside the dish cable.
Good luck..

Yes, happened to me. The rain ran down inside the coax cable.