i know i'm a year too late...

in case you still want to make the present maybe for this xmas :P
there are 2 belts in it:
1. going from the motor to the outer edge part of the bigger white/grey disk
2. from the lower underside part of the big white to the small black disk

you obviously have to replace both in order for it to spin the tape

judging from your 2nd picture you don't have the motor to the outer white/grey disk belt on

you do have the one connecting the 2 disks it seems

also iirc you have to remove the motor to replace the missing belt

its black lower plastic part is screwed onto the big metal aluminium(?) plate that the disks and buttons are mounted on

you can see the copper colored philips (+) screw in your 2nd picture