Over the past few days I have noticed that my oil furnace doesn't seem
to be coming on when we tell it to via the thermostat sometimes (but
not every time). Here's what the chain seems to be:

1.) On the newer digital thermostat (which we have since reset, just in
case), we tell the furnace to come on by raising the temperature (it
seems problematic at night for some reason). Normally you hear an
instant 'click' and the system is heard spinning up in the basement.
Heat then comes on a few minutes later.

2.) What has been happening is no 'click,' no matter how high you tell
the thermostat to go.

3.) Troubleshooting has been as follows: 1.) Pushing the reset switch
on the furnace, which makes no audible sounds or anything--is it
supposed to? 2.) Resetting the breaker (though all the while, power
never seems to be interrupted at all at the furnace) 3.) Having to wait
about 15-20 minutes and then the system seems to come back on most of
the time.

4.) The oil tank indicator says the tank is 3/4 full (Do those
indicators on top of the tank die or malfunction? Do I have a
soon-to-be-empty tank?)

5.) The furnace was serviced and cleaned about 1 month ago.

Before I call the furnace people, I thought I would take a stab here.

Thanks!