In my experience, 90% of all small gas engine problems are carb/fuel related, and almost never the spark, timing, or valves. If the battery is cranking it over, there is almost certainly enough voltage for the ignition to make good spark.
I would suspect bad gas or water in the gas and/or icing in the fuel line. It will take quite a while (like until spring) for an iced carb or fuel line to thaw in a 28 degree garage! Try cranking the heat up in the garage well above freezing for several hours.
Does the gas coming out of the carb smell like gas? If you suspect its bad, drain it all, including disconnecting the fuel line to the carb and draining the float bowl and replace it all with known good fresh gas. A good way to check that the float valve is working and good fuel is flowing through the whole system all in one shot is if the float bowl has a drain on its bottom - you can just drain the whole system from there.
It could also be some contaminant plugged the oriface, jets, or float valve in the carb, but you said you checked all that.
Also, check for any linkage or springs that may have come loose from the carb. Verify that the throttle and chaoke are in reasonable positions while you are trying to start the engine.
- Rick