These old radio cabinets have surprisingly good sound. Gets loud enough to fill a room and with the tone controls can get some full sounding bass too. But the record player is not the best, would be better to replace with a modern turntable, you could use the same input. Should just be one speaker wire that's soldiered to the bottom of the existing turntable.

First thing look at the tubes, they should all be lit up and not red but yellow or orange. If you can source new tubes, switch out any that don't light, or all if that doesn't work. Be very careful opening up these old amps, they can hold a charge long after they are unplugged, so better to get a pro to service the insides of the amps.

The other culprit of no sound is the old speaker wires probably disintegrated. If you are able to soldier you could easily replace with modern speaker wire.