Hi Cris,
Having a completely dead playback head is pretty unlikely. In fact, if you're getting on sound from the one channel with the head selector switch in both the 1/4 track and 1/2 track position effectively doubles the odds that it isn't a head problem.
What's much more likely is that the wiring somewhere between the switch and the output amps has a problem.
Before you or someone else starts to troubleshoot this problem, be aware that the voltages going into the record head and out of the playback heads is very low. It's not a good idea to connect a multimeter to either of them to check continuity since this applies a voltage much higher than the heads are designed for. It will magnetize the heads and it will be tough to demag them afterwards.
I don't know how much experience you have with this kind of stuff but after you're sure that it isn't a switch, pot or the tape, I'd check to be sure all the internal connectors and circuit card connectors are clean and well seated. Many times, the cards will slip a tiny bit in shipping or something and the connection will be sitting on a totally oxidized spot. Moving them in and out a little often times solves this problem for a while. Be careful with the cards since some can become brittle with time.
If you're able to follow the circuit coming from the head selector switch, follow that till it gets to the playback amp section. If that connection is made with a multi-pin connector, try unplugging and plugging it back in a couple of times. If that has no effect, you should be able to make a little troubleshooting jumper system. Just take some uninsulated wire of about the same size a the male pins on the board (probably about 20AWG) and put them into the female connector. Get some jumpers with small hooks on each end (Radio Shack) and connect one end to the wires sticking out of the female plug and connect them to the correct pins on the board. Figure out which ones are the signal wires from the switch and exchange them left to right. If the signal follows the hook/clip, it's almost certainly the switch and it would be a good idea to take the switch apart and clean or replace it. If not, and you end up with no working channels when the jumpers are switched, try cleaning all the connectors leading out of the amp board.
Give that a try and get back to us.