Tascam midstudio 644 powers up and can rewind and fast forward.

Check the belts, inside the unit you should see a rubber belt which is what pulls the tape fast forward or rewind. Some belts with time get loose and slip, they can also break and fall off which will not let you fast forward or rewind.
Open your cassette player and look where the plastic pulleys are located and check for the belts, they might not be broken at all but very loose and slip on the plastic pulley.

The ancient tape is junk. Buy a new one. You might also try slamming the old tape against a wall or desk to loosen up the tape layers. Then FF and RW all the way.

Check too make sure that the tabs on the cassette itself are there if they are gone place a piece of tape over them, then try recording again. It may be a belt issue open the unit and see if all the belts are present cassettes usually have 2 or 3 separate belts one controlling the fast forward and rewind and another for record and play more than likely this is the issue, If so belts for these units are obsolete try searching science and surplus magazine catalog they carry a variety of large rubber band / belts you may get lucky and find one there good luck I hope this helps you

There is either a cam belt that is lose or the flywheel assist can not move the head base due to hardened grease. It needs to be serviced.

Hi,
Does the tape move when you press rewind or fast forward.
If the tape moves for a few seconds then bleeps it sound like a sensor problem.
If it only bleeps when the rewind and fast forward are pressed and the play is ok it sounds like the actuator motor is faulty,this motor enables the rewind and fast forward.
Hope this helps.

Scott has a point. You need to determine what is causing the unit to stop and it could be a bad cam motor belt if it has one or the lack of take-up die to the bad idler or even a dead spot on the reel motor. The reel motor will work normally at high speeds due to inertia but at low speeds as are used in play the dead spot of the motor can become much more apparent.

This sounds like the drive belt has weakened with age. Will have to be replaced.

There is an idler wheel behind the platen ( black plate behind the cassette)..replace the idler wheel.

The guy in texas is Marrs communications

I work at the History Channel and have  a VHS that had the same troubles. I need it desperately for the show I am working on. I tapped it on a table fast forwarded it and presto! Tape fixed, crisis averted. Thank you, Thank you, thank you.

The idler wheel (that only drives the tape in play or scan modes) is slipping too much (very common problem). Try verify this by putting the tape in play then immediately press the fast fwd or rewind buttons to scan the tape. On older machines, the idlers used rubber friction tires - on newer ones, a clutch. Either replace the tire or increase the spring tension on the clutch.
Hope Ya Fix It.