My crawl space cover broke on a recent windy night. Ever since then, my furnace either won't kick on at all for long periods or it will then kick on and off like it can't quite "catch" and come on. On those occasions that it does finally kick on, it only blows for 2-3 minutes and the air feels cool, not warm at all. Overall temperature in the house is in the mid to upper 50's at night even though the thermostat is set on 69.

You need to keep air from blowing on the heater. If pilot goes out, heater will not operate.