Goodman GMP100-3 Nothing Happens!
Not as familiar with Goodman as with other brands, but ussually a solid light indicates that you have power on to the unit. A blinking light will generally tell you there is a call for heating from the thermostat. Is it possible that your thermostat isn't making the connection to the furnace? It is easy enough to take the stat off of the wall and jumper the 2 wires together. 1 is connected to the R terminal on the stat and the other is connected to the W terminal. R is your 24 v power to the stat, and W is the call for heat that takes that 24v back to the furnace to tell it to fire up. By putting these two wires together you are making the call for heat. That is what I would try first.
You may have to turn the power to the furnace off for a couple minutes and back on agin to clear any codes that may be in the memory, if there is another problem, so that you can see what is going on from there. There should be a chart on the inside of the furnace which will tell you what the LED codes mean if they may be different than what I expect. They will also be in the service manual if you still have it. The roll out switches ussually protrude out from the body of the switch by about a 1/16th of an inch or so, and when they open ussually you can tell when they reset when you push them in, and you may even hear a slight tick.
Try that and get back to us if you need more info.