Arcoaire furnace hums but won't turn on, green light is steady on (No Blinks)has work at least once this season

Try replacing the batteries in the thermostat, if they get week it won't call for heat when it says it is. If that doesn't work post back. Also, you should post your question only once. ;-)

Weak not week, lol

Thanks I replaced the batteries also tried jumping the wires at the furnace, still just a hum from the capacitor, no sign of a glow from the ignitor. AC and blower work fine?

Capacitor shouldn't hum... sometimes a transformer will hum though. You say you jumpered R and W at the furnace with no success? If so then you will need a multimeter and of course be able to use it. If those are skills that you do not have then I suggest calling a qualified technician as there are a variety of tests to be performed now.