With a cartridge installed, try taking readings at the RCA plugs for both the L & R channels, the cartridge should measure as per this topic:viewtopic.php?t=22754
IIRC, I was able to measure cartridge resistance at the RCA plugs when I was troubleshooting my SL-10 (to find why I had an intermittant channel cut-out) while the unit was off.....
Page 23 of the service manual shows the block diagram of the muting relay (lower left of the page) and paging directly down to 24 shows RL1 physically on the circuit board.
If you still do not get any sound, you will have to open up the SL-7 while off and try giving RL1 a couple of sharp taps. Hopefully this will free / unstick the relay.....
While you are in there, clean the connectors CN 302 & CN 303 with some contact cleaner.
Hopefully, this will square away the SL-7.
If not, make sure there is 12V energizing the coil and you can try replacing RL1:http://www.encompassparts.com/products/?MSCSFDSC07-01
Or eliminate the relay and hard wire the phono input to the phono output on the circuit board, refer to page 24.
Fred and my bet is a sticking relay which you should be able to unstick with a "hit with a hammer"...... albeit, a light one.....
Music is Everything....Except Predictable....WFUV Fan.