here goes -
the signal path from the stylus tip to the phono outs does not connect to anything at all inside the technics turntable apart from a junction box under the arm -
take the deck apart and check for some solder that has wiggled loose on 1 of the earth wires - find out what channel the hum is from(left or right) and look at the tone arm wiring diagram to find out what one it is (green/blue?? havent touched a set of technics for about 5 years now so im going from memory)
the wires are really thin and a pain in the arse to resolder so it might be better to take it to a music shop to get it rewired properly - it isnt the actual turntable bit that is at fault because that is totally seperate from any audio cabling
have fun - i done mine pretty easy when i had it go to shit :)
while your there - give em the pitch +-16 makeover too with the little cross head plastic adjustmant things on the circuit board near the tonearm bit -but remember to set the brakes up also to make up for the extra speed u get