Yes,
The belt is the most likely cause, IMHO, since I've replaced many capstan drive belts on my many Tascams, and this is quite common on older Portastudios and other decks, (R-R's included).
The belt you need might be available from an electronics supply store that has VCR/cassette style belts.
The manufacturer of these kinds of belts is: "PRB, Projector-Recorder Belt Corp., USA". You might find them on the web.
The PRB designation for the belt you need will be "FR XX.X", such as "FR 12.5", meaning 'flat rubber belt, 12.5 inches", but verify your own belt size in inches or mm's.
I can't quote the size to you, but you'll need to remove the belt, and take it down to your electronics parts dealer, and measure it (in-store) and match the old belt to a new belt, (flat rubber belt), which, BTW, should be a few mm shorter than the belt you're replacing. These older/worn out belts, by definition, are
s-t-r-e-t-c-h-e-d o-u-t.
Any electronics store that has these belts will usually have a little gizmo that you can measure the belt on (in a loop). Lacking this measuring device, you may also cut the belt, and measure the total linear length, with a ruler or measuring tape.
A slightly wider-beefier belt is ok, too, but just make sure that the belt you get is a few mm shorter (length/loop) than the one you're replacing.
Tascam Parts dept. will take phone orders w/credit card, and ship the part to you, too. This is very expedient, and the belt you want is not expensive.
Tascam Parts is @ (323) 727-4840, and they are glad to help. Just tell them your Tascam model #, and they'll find the part #. I call them frequently. Some people recommend email to 'parts@tascam.com', but I've heard email is not too effecient, and calling is very immediate. They'll ship overnite, 2 or 3 day, or whatever UPS method you're willing to pay for.
Remember, the capstan drive belt is easily accessible by removing the 488's bottom panel, and half removing the bracket that holds the capstan flywheel. Easy money.
Good luck, and as you endeavor to replace this belt, you will probably find it's 'not too hard'.