Take the tape off the 388 and do the following:
1. Raise the right tension arm all the way up. Does the capstan shaft spin (that's the metal shaft about the diameter of a pencil on the exit side of the headblock)?
2. If so, when you hit PLAY does it keep spinning AND does the pinch roller move and press against the capstan shaft?
3. If so, with the 388 still in PLAY and you still holding the right tension arm up, lower the right tension arm about halfway. Is the takeup reel table spinning counter-clockwise and the supply table spinning clockwise?
4. Do FFWD and REW work with tape loaded?