Warm way to check your transformer: plug into an outlet inside and test if you get 120V on the output side. If not, well that's that. If yes, then maybe it's your block heater? Testing by touch on a cold day outside might not be too helpful...
(measure current with ammeter, but it will need to handle the load of around 10-20A if it is working)
Try plugging it into a current monitor and check if you are drawing any current. You should see many amps draw if it is working.
Dave
Times 3 Friis..
In the end..at least you'd know everything Is, or Ain't working.
You might check the plug and cord leading from the plug-in to the element too.. they tend to get weather worn-cracked over time. I've seen the plug lugs burnt, from not being heavy duty enough.
Joe