If there was a smell like something plastic burning it may be that something just actually burned. It does not have to smoke like a chimney (sometimes it does though - depends what is burning)... If there were no strange noises and it did not seem to run any different than usually - most likely the motor is still fine. I would inspect the cord really carefully but to do any more than that you would have to open the unit and inspect everything else.

If you chose to do so – open the Rainbow and hook up the motor directly to a power supply (hold on to the unit as it will move while starting) – if it runs then problem is in wiring. Test the cord with a tester or bulb, then the switch (or 2 switches if this is e-series Rainbow). Make sure all wires are intact. There is not much to test so you will get it done and find the problem quick.

This is messing with electricity and subjecting you fingers to potential hazard by exposing working motor so do it at your own risk and be very careful and if anything goes wrong do not blame me :-)