2016 Toro Power Curve 1800 (electric) - sounds like motor is running, just put a new belt on, but the paddles won't spin. Any suggestions?

If you can hear the motor running it probably needs a new drive belt and if the motor isn't running there is an electrical fault that must be checked by a suitably experienced person.

Some of the older power scrubbers/polishers I have seen didn't have a belt but used a simple but substantial gear drive system that gave no trouble in my experience.

It may only need unplugged to reset rather then taking inside.

Likely it's a thermal switch. Try running with out moving snow and see how long it runs.

Visit the on-line store, know as reliable-store, they have the repair manuals. I'm sure you will get the solution of your problem.
Best Manuals

adjust the cable at the bottom will work again

Yes. Adjust the tension or perhaps you need a new belt or cable.

see this causes and fix it. God bless you
Motor Coupling If the washer won't spin or agitate the motor coupling might have failed. The motor coupling connects the motor to the washer transmission. It is designed to fail if the washer is overloaded in order to protect both the motor and
Drive Belt If the washer won't spin or agitate, check the drive belt. If the belt is broken or if it isn't tight on the pulleys the washer won't spin or agitate properly.

Drive Motor If the washer won't spin or agitate the drive motor might be defective. This is not common. Check all of the other related parts to this symptom before replacing the motor. If the motor is visibly burned out or physically damaged, replace it.

Stator Assembly If the washer won't spin or agitate the stator assembly might be burned out. The stator is essentially one half of a motor, it interacts with the tub by creating a strong electro-magnet. If the stator burns out the washer won't spin or agitate. Check the stator for continuity. This part is often misdiagnosed.

Door or Lid Latch Assembly If the washer won't spin or agitate the lid switch assembly might be defective. This is a very common problem. The lid switch assembly can fail either mechanically or electrically. Test any electrical switches with an Ohm meter for continuity. The switches should have continuity according to their design.

Door Lock Motor and Switch Assembly If the washer won't spin or agitate the door lock assembly should be checked. The door lock can fail either mechanically or electrically. Test any switches on the door lock with an Ohm meter. The switches should have continuity according to their design.

Motor Control Board If the washer won't spin or agitate the motor control board might be defective. The motor control board provides power to the motor as well as direction and force. If the motor control board is defective the washer may not work at all or function properly.

im assuming you dont here any grinding, start by tightening the cable ( loosen the cable mounting bolt slide the cable towards the engine, make sure you leave some play in the cable so its doesnt engage constantly and re-tighten ) this is most likely your issue however if you re-test and get grinding you either need new drive gears and wheels, new transmission or possibly both, you said it does something just not powerfully this pretty much rules out your belt, highly doubtful its that worn out and if it came off of a pulley it would do literally nothing, however if you tighten it and the drive is almost normal but still weak you do have a worn drive belt

Can you pull start it? If so,you may need a new starter gear,about $30,they're plastic & wear out.

Is there an easy way to install rotor blades on a Toro Model 38430 snowthrower?