My other DCC730 works correctly now (DCC730 head/pinch stuck, drawer does not open but tape plays - #11 by Max); I looked at this one closely for comparison, took out the capstan flywheels, too to properly compare.
It does everything (placing the head/pinch rollers on the tape, fast-forward, rewind) except for moving the tape while regularly playing.
The only movement happening to the tape when pressing play is a few mm from the head and pinch rollers pushing down. I will carefully check everything, and I am sure I will be able to resolve it, but maybe one of you can tell me what I could look for, i.e., which cable might be loose.