At a glance it looks like everything is set ok in your firmware but it doesn’t look like you’re running the same Marlin version that is posted on this site’s homepage so it’s hard to compare everything.
3 possible troubleshooting options:
1) Make a backup of your firmware which I’m assuming you’ve done since it’s posted here. Download the version on the vicious1 homepage and modify the pins_RAMPS_13.h or pins_RAMPS_14.h file , whichever has your fan pin definition, to change the fan pin over to 44. If that works then something is wrong with your firmware and I’d suggest just sticking with the newer version instead.
2) Try switching fan output to a different pin like number 42 which is right next to 44 on the aux2 terminal block. It’s possible you damaged pin 44 on the MCU when you had that soldering short that you described in one of your earlier posts.
3) If you know basic Arduino sketch writing you can backup firmware and write a quick sketch that will configure pin 44 as analog pin and then send analogWrite commands with different values every few seconds to see if the pin is working for sure or not.
Any of these options should help you figure out what’s going on.