My Teac 4070G reel to reel tape deck rewind and fast forward functions work, but the play function does not. Any ideas? Could it be a circuit?

It is common after all this time to have pinch roller linkage not moving and I was even doing them in the 80's when at the factory service. If the Pinch roller does come up and is free to move then the next item would be the capstan belt. Check to see if the motor remains turning. If it stops then either it needs oil or a new motor run capacitor. The model was one from the early parts of the 70's. May have also been around at the Vietnam war exchanges. That is a lot of years to have parts on.

Without actually seeing your Teac reel deck, i suggest you verify that all fuzes in the deck are good..not blown. Also with a tape correctly installed..ensure that left and right tape tension arms are held under tension/ closed by tape tension, also ensure the capstan shaft is rotating... look in back to ensure the capstan drive motor is running.. if yes, and tape still will not play... problem could be a stuck/failed solenoid, dirty or corroded push buttons, or corrosion on contacts where rear circuit boards/plugs insert into other boards.