I very highly recommend the MicrAir as well. The Dometic thermostats can't even start to compare.
I'm thinking if the thermostat was working without the cover (using your fingertips?), then you put on the new covers and lost the furnace option, it's got something to do with the covers or something that happened when you put them on. The reset recommended may get it back. Pulling a fuse to it or opening it and pulling the 12v+ off should also do it. If those don't work I would pull the cover back off and try it like you were using it. If that doesn't work I would order the MicroAir
. Did I say it works great?,,
My comments are based on my assumption you have the infamous Dometic CT thermostat.