RichMA,
And the search begins.
Does the pump not prime if you close the skimmer(s) and use the main drain only as your source?
Is your water level high enough in your skimmer?
Is the skimmer door (weir) moving well with the water? If it sticks in the upright position, it will block water from getting into the skimmer, and air will take the place of water in the line.
Do you have a suction side pool cleaner in the pool? If yes, disconnect it or remove it. The hose may not be air tight. Does it have a leaf canister? The canister may not be well sealed and sucking air.
Did you lubricate the O-ring on the pump basket lid?
Is there a hairline crack in the pump basket lid?
Do any of your valves require lubrication? Some types of older ones do.
Have you any low-priced ball valves? They can fail and pull in air through their handles.
Have you poured or hosed water slowly over every pipe joint and valve and lid while watching the pump basket for the beginning of a prime?
Have you tried shaving cream as well?
Perhaps if none of these are the solution, maybe the impeller in the pump is not turning, and the water simply isn't being drawn in at all.
Anyone else out there, make your suggestions, too.