Goodman furnace that was working fine until i went out of town for 4 days, turned off the power, and now cannot get the electric ignition to work [although it did fire up for 1-2 seconds the 2nd tim

https://hvac-boss.com/troubleshooting/goodman-furnace-error-codes/

According to this page, you can usually fix this 4 blink diagnosed problem by changing the air filter or tightening wiring (which it has a cautionary warning about tightening such too much) and checking the flue for blockage. The furnace has activated the primary open limit circuit.

Here is a troubleshooting page about the Goodman just blowing cold air: https://temperaturemaster.com/goodman-furnace-troubleshooting/#Goodman_Furnace_Blowing_Cold_Air

Poor air flow in the Goodman caused by blockages can result in the tripping of the rollover switches which would cause it to blow cold air. That is a safety measure. You don't want gas furnaces burning with insufficient air. Think carbon monoxide. Besides the air filter, the flame sensor or the burner could be dirty. The idea of trying to DYI that cleaning job is rather off putting. I hope changing the filter would work.

I trust it is not a fuse in the pilot flame sensor circuit blown. A repairman has the voltage testers for checking the electronics involved.

I can empathize with this. My furnace, another brand, went out recently. The repair man didn't know why it went out but simply adjusted a handle controlling gas flow to a position slightly different from what was recommended and it worked. All for $200.

https://www.repairclinic.com/RepairHelp/Furnace-Repair/36-377--/Goodman-Furnace-Troubleshooting

https://www.youtube.com/watch?v=zO1jKqwXu8s

https://www.goodmanmfg.com/products/gas-furnaces

Check flame sensor , check hoses to pressure switch not split etc

There could be other problems but check and see if your igniter is not burnt out. Ours did that and tried to ignite for two days and then I found I had to change the igniter.

Check if 24 volts is being sent from the board to the gas valve, if not the board is nad and will need to be replaced, if there is 24 volts at the gas vlave terminals then the gas valve must be replaced.

https://www.repairclinic.com/RepairHelp/How-To-Fix-A-Furnace/171-377-1442688-/Goodman-Furnace-not-heating-GDS80703AXBC
Check out this site. Has DIY videos that cover your issue.

Power is there, or no lights would blink. Steady blinking or flashing three times, stop, three times Etc

it sound slike the presure switch is not working , if it is not lighting try jumping it out it may work some times you can fool it in to working

had similar problems with same furnace. I think the 3 blinks is high limit event. either way with the power off to the furnace remove the board from the 4 clips holding it on one at a time then turn it over and look at it you will be able to tell if the board is bad because it will appear scortched and the resin will be bubbled up where it went bad. replace board and you will be fine. went through 2 in 2 years all of a sudden they are being made by a different company from the original and the 1st replacement. now all is fine. Take a good picture of the board close up so you can reconnect all the wires properly. Friend of mine got it from a wholesaler for $55.00

The blink codes are differant on every furnace. Read your code on the schematic found on the inside of the door. You most likey have a dirty flame sensor. Under the burners you should find a "single" wire going to a connector. This will be to the far left or right. Just opposite of a "two" white wires going to the hot surface igniter. Remove the 1/4 inch screw closet to the single wire under the burner. carefully pull out the flame sensor. Clean it with a small piece of sandpaper. Re install it. This should fix your furnace. KEEP IN MIND Goodman GMP models are noted for defective heatexchangers. Pull out the blower assembly and turn it over. If small rings about the size of a dime falls out.... this furnace is unsafe and should replaced!

pull the rubber hose off the pressure switch. and blow into the Induced draft motor housing if you cant you can pull the hose off the IDM and try to clear it with a small paper clip. reconnect and try again. you can also get the flash code off the board while the unit is running but not working.