Furnace not turning on

Hi all, I'm a newbie at troubleshooting furnace problems, so please bear with me........

I've got a home gas furnace that's failing to consistently turn on when it is supposed to. Here's what I've done so far:

1) Checked circuit breaker for Furnace - OK 2) Reset the furnace by following the instructions inside the furnace to turn it off & on - Done 3) Checked thermostat - OK. Removed thermostat and manually jumped the two wires to make sure that furnace is turned on. Nothing happens to the furnace. 4) If I hit the exhaust(??) blower - not the main blower that blows warm air through the house, but the one by the flue pipe - the blower will start to spin and in turn lights up the igniter. I'm not sure how this blower has anything to do with the electronic ignition system, but this blower unit must work before the igniter lights up. I should also note that this blower unit has been squealing over the last while when it first starts up but I didn't think much of it. 5) Once I get the unit up and running by tapping the blower, it may continue to work fine for another half a day or so. 6) When it stops working, I have to repeat step 4 again. Seems like its going to fail for good soon.

I hope this makes sense. Can anybody please tell me what the problem might be?? and what can I do to fix it?

Thanks,