[35Z5]

Congrats.

A disconnected loop antenna can cause hum on AM, the FM should have a length of wire or maybe be coupled to line cord. 

FM in these older radios was persnickety when new. Could have a defective tube or bad component but be very careful how you proceed, lead dress is important, move component location and it may never operate. Not to scare you I've been working on these things since the '60s and walk a wide path around most older FM sets. 

The filter caps won't keep set from operating, though 100 is a bit much for a 70. At worse it could cause rectifier tube failure..

[apERNA1985]

Ok, if I get you a few pictures of the back could you help me rewire it?

[apERNA1985]

I went through the rider diagram this morning and ordered all the tubes it says deal with FM

[35Z5]

Per the schematic, loop only has two connections, those will measure a low resistance when checked with a ohm meter. Third is for FM, should be easy to sort out.