By removing all fuses except F6 (AC Mains IN) you have isolated the transformer from the rectifier. The fact that F6 now survives indicates the transformer and wires to the rectifier are not shorted somewhere.
Now you need a 3Amp Circuit Breaker, or a handful of 3A SLO-BLO fuses.
With only F6 installed, power up game. The fuse should survive if I understand correctly. Power down.
Install F5. Power up. If both fuses survive, now you will have visual confirmation if the game is actually a ON or OFF.
Now continue replacing the fuses with the correct rating with power off each time.
You should run into one that pops the Mains again.
Let us know what your investigation reveals.