No qualifications. I'm definitely gonna get outside help. Do you have any recs for how to get this set up to sound as quality as possible? I'm ok with replacing the TT. I'd really love to keep the speaker and have it wired to the TT. The Radio wiring is a disaster. That's very last on my list to fix.
You'll need a pre-amp for the turntable, and it has to be specifically made for TT. Not just any sort of generic pre-amp will work. Then you'll need a power amp between the speaker and TT pre-amp. You have to be sure the speaker will work with the amp you have. They did weird things back in the day. Just because it's a speaker, it may be some odd impedance that was made only to work with the specific radio. Speakers and amps were't as universal as what we are used to today. Have you tried testing the speaker with a 1.5 volt battery (D-Cell) to see if it even makes noise?
If you replace the electronics, you may also have to replace the speaker with something more suited to the new amp.
When I suggested replacing the electronics, what I had in mind was to find a new, or newer and working, AM/FM receiver that also has a TT input. The TT input will include the TT pre-amp, and you'll have your radio and amplifier and it will do all of the switching in one box. If you can find something that will fit in the space then it's just a matter of probably doing a bit of modification to mount the AM/FM/TT system. It pretty much sounds like the old electronics is toast, and dangerous toast at that.
Your new electronics will likely all be stereo, but that's OK. You can either mount two smaller speakers in place of the one, or if lucky, the electronics will have a mono switch and you can use one speaker, hopefully the one you have or the new one. There are other ways to get stereo down to one channel, but let's see how far this goes before we cross that bridge.
I'm sure others will have some good ideas for your project and come up with even better ones than mine. But given the lack of experience and condition of the electronics, it sounds like restoring the radio/TT amp may be a bit more than you will want to take on.
You've got a nice piece of furniture there and I wish you luck with the rest of it.