I was given two 4-tube fixtures, which when removed from old location were supposed to be working fine. I have the same problem with both. This fixture has a Magnetek Ballast 780-LR-SLH-QP. It has 4 wires open. 110v applied to the Black and White lights 2 tubes. At the other end of the ballast are a Black (with white stripe) and a White (with black stripe). 110v to these do not light other 2 tubes (all tubes have tested good in a different fixture). What is the wiring configuration with this ballast to get 4 tubes lit?

Assuming that the ballast is not bad (in BOTH fixtures?? ), Can this ballast be wired to turn on 2 tubes (for lower light) with one switch, and have a 2nd switch to turn on the other 2 tubes on occasions when higher light is required?

You can wire that fixture to light just 2 lights if you would like. Each set of black/white would need to pass through a separate switch. You could also join the two blacks and the two whits to control all 4 bulbs with just one switch, its really up to your choice.