Hi
Where there's smoke, there's fire...or at least was.
There aren't many parts here that can fail. Electric motors are usually pretty sturdy, so the main culprits could be the controller or the batteries. First thing to do is to visually inspect the parts. If there was smoke, there was heat...so check for discoloring and warped plastics.
If you have a voltmeter, check if the batteries are actually full after you've charged them. My guess is one or both batteries have died.
good luck
Schwinn Customer service: 1 (800) 626-2811
www.electricscooterparts.com/schwinnscooterparts.html
Above is only one example of parts availability .
You will likely have to call to get the manual.
generally speaking, you should clean the air filter, check, clean and/or change the spark plug and clean and set the carb. Mostly these faults contribute to these kind of performance. (These simple and cheap maintenance steps are easy to do on your own, however, in this case, I highly recommend visiting a mechanic or asking for help from someone who's more mechanically savvy. )
Always RED wire to the positive terinal of the battery and Black to the negative terminal of the battery.The other way to make sure of the wiring is to follow the wire frm the starter solenoid switch this will always fit to the positive side of the battery and follow the wire from the either the engine or frame (usually is black in color) to the battery box and this one is always for the negative side of the battery.
with the spark plug out and the valve cover removed; place a screwdriver into the spark plug hole; turn the crankshaft until the valves are all the way up and, not moving as the piston just starts to go down in both directions; (use the screwdriver to see this) this is TDC or, top dead center now; you should see symbols on the faces of the cam gear and, the crank gear and, two places on the chain; line up the chain symbols with the gear symbols chain symbols facing out and, install the chain. by the way they make a kit for stripped sparkplug holes an auto parts store will have it in case you need one again.
Check your charger with a meter and see if it is putting out the correct voltage for your scooter battery. If it is, you probably need a battery, probably so anyway after 2 years. Good luck!