Ooh... those are about the pickiest ones there are. I have 3 of them, and only one works 100% properly.
The problem with these is, they use two motors - one to pull the tape in, and one to actually play the tape. When you insert a tape into them, it moves an arm away from a little switch - this tells the deck a tape has been inserted. The deck then pulls the tape in the rest of the way and plays it.
What has probably happened in your case is the tape insertion switch is dirty. The deck needs to be pulled apart to have that switch cleaned. It's pretty easy to find - it's on top of the main drive motor (the larger of the two).
But that's just one possible explanation - these decks are so finicky it's really hard to say without taking the whole thing apart to see what's up. One of mine kept changing tape directions due to a dead reel sensor and one kept cycling on and off because the tape eject arm didn't push on that loading switch hard enough. I felt real lucky when I found the one working one.
I managed to fix the constant cycling deck, but not completely - for some reason it now starts playing at double speed. As an electronics tech, these are some of the most aggrivating tape decks I've ever worked on.
I have a yard run coming up on the 9th of next month - if you want I can look for another one to fix up (since I have two parts decks). They only cost me $20 or so at the yards where I go. Problem is though, I'm in Canada - shipping might make it not worth the trouble.
Edit - btw, Xtrempickup's TC deck will be the same one you have
