If it's a big airport there will be hangars or maintenance facilities. Many have diesel powered emergency generators on site. They may also have a dedicated battery charging facility. Lead-Acid batteries are stored in a fully charged state, Ni-Cads either but you may find some usable units in the battery store room. Get the hangar generator up first and you may be able to charge an a/c battery to full.
...all APUs/jet engines need some kind of external power source...
Not necessarily. Some smaller turboprop a/c can start the engines from their own internal battery.
If you get the APU running you're laughing.
The B777 has a pneumatic starter on the APU in addition to an electric starter. So if you can get an air starter unit running and a partially discharged battery on board the a/c, you may be able to start the APU.
Refuelling will also require at least a working battery. But a fully powered a/c would be better.
Do not attempt to use a B787.
