This could be so many things on an old deck; lubricant migrates or turns to goo, pinch rollers and idlers dry out, belts dry out, caps go bad and cause the speed feedback to fail, motors get flaky, some debris gets into the mechanism. Really could be a lot of different things.
The associated squeak coming from the capstan area makes me think that the capstan bearings need to be lubed or replaced. I don't know if they are sealed. Don't go dripping WD40 or regular machine oil in there. There is a specific type lubricant that is recommended and there is a specific type of grease for plastic gears. If lubricant has dried or migrated, you can still have a working machine with an intermittent squeak when the mechanism drags until the mechanism eventually wears and the problem is persistent.
If you own the deck, it might be worth it to you to buy the service manual. The service manual for my deck cost about $80US.
You might want to check around on
tapeheads.net and see if there is some info there specific to the Dragon but there will be a lot of more general info.