I would like to know if it is possible to run electricity 1400 feet from a 100 amp service and have enough ampreage to run a few 100 watt lights and a well pump.

The distance you want to run the cable is more then likely cost prohibitve. Not to mention the electrical design.

For example, if all you need is 60 amp, 240 Vac, at 1400 feet, you would need a cable that supports 400 amp. That will get you 60 amps.

You have a service of 100 amps, so your entire site would have to be re done.

Please consider a solar source adjacent to the shed. They also are not cheap, but probably much cheeper than a 1400' run.

Depending on pump size and voltage. Assuming 1 1/2 hp pump and 240v a #3 copper or #1 aluminum will probably work. Really need to know max amperage of the pump (starting amps).

#3 copper or #1 aluminum X 1400 " = $$$$