It would be "the capacitor" as most of those motors in the smaller blowers do not have the start switch because it costs more. They use a single capacitor for start and run. And it is not a high quality cap by any standard. Not moisture proof, for instance.

 

automotive engine oil will work well

For motor bushings I use transmission fluid. Has its lubrication qualities but also has a cleaning property to it. Used TF on my swamp cooler for decades and it has lasted. My son-in-law now owns my old swamper and I've instructed him to use TF as well. He's got it 3 years now. Also have used TF on box fans and other motors that have bushings, not bearings, bushings.

As for the fan - spinning it backwards - if it runs then somehow the start cap has become disconnected. Back on one of my earliest jobs working on an assembly line in a HVAC units manufacturer, guys would snag a fan and zip wire it to keep themselves cool. As a joke we'd pull the plug and then disconnect the cap. Plug the fan in and spin it backwards.

So either the cap has gone bad or has become disconnected by either a plug coming off or a wire breaking. There's even the possibility the break could be inside the motor. Hope not. Hard to find and fix. But for a certainty, I'm not the motor expert here.

 

I found that motors, or at least the capacitors of such motors that originate from China are often the culprits.
Those that purchase imported machinery from there, often experience problems not long after some usage.
I always recommend the N.A. or other western source replacement.

 

MAXIS RIGHT!!! and just because the cap is not adequate to start the motor does not mean that it has totally failed. So I very much doubt that a reverse spin will run it the other way.