The suggestions above seem like the most likely to me. But if those check out okay and are not the problem, the next thing I'd check is my LPG pressure. The regulator next to the tanks can accumulate oil over time and the pressure can drop below the desired 10.5 water column inches. At least, it did on mine, dropping to about 6 inches. Stove, oven, and fridge all continued to work okay on this reduced pressure.
I will say I find it odd that the igniter runs long enough that it's still clicking away after heat is (or was) coming out the exhaust port. Although you're no longer getting any heat, the fact that you got some while the ignitor was running suggests to me you either have an obstructed air intake or insufficient LPG pressure. Low LPG pressure might show up in some yellow flame on your stove burners.
When you get it fixed, let us know what it was?