Man, that's a lot of hand winding!
Probably covered before, but you want to make sure it's not a "sticky" tape that's prohibiting the rewind function. Sticky tape is to blame for many transport issues, as it's proven over time.
If you feel adventurous, there's a moderate disassembly to take the face plate, deck plate, or whatever you want to call it, from the face of the reel-to-reel transport. Once under this cover, you'd want to verify the brakes are releasing fully when tape's put into motion.
Beyond that, I'd venture to say that if you suspect a bad motor, it's likely one bad, or a pair of bad drive transistors, (2 transitors drive each reel motor), more than the motor. Just by probability. Unfortunately, that's a techy repair that doesn't lend itself to basic DIY efforts.
The description of "tries to get going but stalls" has me suspicious of bad tape. It depends on how much it "tries" before giving up. If it goes a second or two, I'd suspect bad tape (or servo adjustments). If it moves a split second and goes entirely limp, losing tape tension, I'd suspect motor drive transitors.
(As mentioned), the reel/servo electronic adjustments could be off, which would directly affect the FF or RW function. As a rule of thumb,... the centers of the Left and Right Tension Rollers should intersect on a plane that's even with the tops of the Idler and Tach roller, left and right respectively, when in Play mode. Picture it,... or consult the manual. If the rollers don't have this configuration, it would indicate that the reel/servo electronics need adjustment. The good news is it's relatively easy. Again, consult the manual.
The 388's a nice unit, but there's a lot going on in the box.
/DA