Furnace Blower Motor fan hums but wont start
Yeah, could be the capacitor.  A good quality multimeter with the ability to test capacitance can check it for you.

Discharge the cap, and remove it for testing (be sure your furnace is off).  Then, set your multimeter to the F/uF setting and test it.  The cap should show the cap rating in micro Farads (uF) and a +/- percentage.  The reading should be within that range.

That said, I had the same issue.  Cap was out of range (measured 9.6 on a 12.5 +/-6% cap).  Replaced cap, motor seemed fine, but shortly thereafter would sometimes not start.  I pulled the motor out, and dismantled it.  The commutator was gummed up a bit, so I cleaned it.  Worked ok for a bit, but the furnace would still sometimes limit out (probably because the motor wasn't starting).  Ended up replacing the blower motor, and it works fine.  Furnace was 23 years old, so I guess I can't complain.

Moral of the story is that it could be a combination of both.  And, btw, if you replace the motor, always replace the cap, too.