I came home this evening to find my luxair furnace running, but only cold air coming out of the vents. The led light is flashing 4 times. I replaced the filter, turned the furnace off for an hour, but the problem persists.

The owners guide indicates the 4 flashes indicates that the auxiliary limit switch has opened its normally closed contacts. It further states that this may be due to an incorrect firing rate or faulty blower motor, among other reasons.

Any ideas on what is causing this problem, and what the costs to repair would be?

The aux limit switch is usually not that expensive, 10-50 dollars. There should be 2 wires going to it . The best way to check and see if the switch is open is to use a volt ohm meter and check for continuity. If the swich has continuity, then the switch is good. The furnace is blowing air, so I don't think the blower motor is faulty. The aux switch is the best place to start. I hope this helps