At wits end......

Do you have a voltmeter? This should answer the question if your charging system is good or not.
- Measure the voltage right across the battery terminals while not running and after having set for 30 minutes or more; a well charged battery will typically show about 12.6-12.7 volts.
- And for a running test, measure the voltage across the battery temrinals at a fast idle, and see if you have at least 14.0 volts or thereabouts.

And what fuel pump brand and model are you using?