What switch at the furnace are you using to turn the fan "on"? And when you say it turns on but does not stay on does it turn slowly then to a complete stop?
On my unit I could hear the relay kicking in and I was able to measure 115v to the high speed (black) wire to my motor. It would spin up slowly then fade to a stop and my coil froze as a result.
If this sounds similar to your situation start with the "Run" capacitor that is usually mounted near the control PCB or follow two leads from the motor that go to a little silver box. Find a HVAC supply store or a store that sells motors, generators etc and purchase the run capacitor and install it.
I just did mine and saved me $500 cuz I know the HVAC Tech would have sold me a new motor
let us know what you come up with