I have a York Diamond 80 central air unit that won't start. It's nine years old. The outside condensing unit runs but the inside blower will not start. It makes a light humming sound.

Possible a bad capicitor,you need a special tester to check it of either just replace it with a exact replacement, if you do it yourself, Cost maybe $10,

Also check PCB, it might have bad solder joint on the relay.
Resolder and it should fix.
I had same problem and fixed it.