I don't think it's likely that the motor is in trouble just by having the belt wrong. It would require more physical damage to cause the motor to play up. Having said that the motor could have been in trouble before you touched the belt. But you do need a new belt, all you need to do is measure the diameter of the belt in mm. You might also need to measure the width. To find a new belt put the words "turntable drive belt XXmm" into Google. You can add Crosley to the start, but many belts are universal. Your measurements don't need to be spot on with the diameter, so if you have measured it at say 95mm, a 90mm to 100mm belt will do the job. However fitting the new belt is a different matter. You need to know the correct way, or the speed might be wrong. I can't help you with the fitting of it, so you will need to check how to do it. Some makes have YouTube videos of the fitting. I would just look for Crosley and see if any look like your model.
If fitted correctly and there's a problem with speed still, then you should look more closely at the motor.
It sounds like you have too much pressure on the tone arm. Check the underside for springs. You might be able to remedy the problem the old fashioned way. Tape a coin onto the top of the tone arm, as far to the rear as possible. This will eliminate some of the downward pressure onto the record.
Turn the arm that holds the element and needle careful to the far right and the turntable will spin. This is a safety feature for protecting the needle.
It sounds like the belt driving the unit might be out of place or connected wrong. It could be the belt is slipping caused by wear and thus needs replacing.
This is an internal circuit switching failure that requires a Crosley servicer to repair. You may have difficulty finding one because Crosley is just a brand name attached to equipment manufactured offshore.
