MD83FO
It pretty much depends on what sort of scenario we are considering. Let's consider dispatch with APU INOP to a remote destination where only 1 GPU/ASU is available and -surprise!- they fail as soon as you arrive at the gate. As others have said, I take it as an extremely unlike situation in standard commercial airline operations, but with that being said let's imagine You are also lucky enough to arrive at night time with this lovely scenario.
- you will need to coordinate with ground staff a disembarkation with the port engine (ENG 1) OFF and ENG 2 ON. If they are happy with that, great, if not then you will need to shutdown everything and use the emergency exit lights but you will be stuck wherever you are.
- once the disembarkation is completed, you need to restart ENG 1 in crossbleed and shutdown ENG 2 to allow bags offloading and refueling with one engine running (SUPP FUEL).
- when you are done with that, restart ENG 2 in crossbleed and shutdown ENG 1 to allow pax embarkation on the port side.
- you are now ready for pushback or taxi and can start ENG 1.
I reckon this sort of scenario could possibly happen only if you are extremely unlucky (no apu, no gpu, no asu) and conducting a charter flight for a humanitarian purpose and need to get the hell out of there ASAP. Not our ordinary day at the office as airline crew members.