The plugged drain would not keep the refrig. from working. If on Elec. or gas it will take about 8 hours or longer to get cold inside. How long are you waiting? Usually plugging it in or turning it on the day before you need it and it will be ready to use.
If using propane it will only try and light 3 times by it's self so if you have air in the propane line it will not light and you will need to turn it off and try and start it again. The same goes for the furnace.
After turning on the propane at the bottle start all the burners on the stove and that will speed up clearing the propane lines of air.
The refrig. also needs 12 volts of power to work (furnace also) so if your batt.s are low re rig. and furn. will not work.