Ok, I assume those "out of order" valves are stuck open? and go to the pool return eyeballs? When you open the pump strainer lid the water should drain back down the pipe, if water drains before you open the lid you have a leak somewhere, often is will just be the gasket around the strainer lid that needs to be lubricated with silicone lubricant (not silicone adhesive and not petroleum jelly), when the pump is turned back on it should be able to prime itself within a few seconds, if it does not prime within 20-30 seconds you may need to pour some water in before closing the cover to get it primed, some water will stay in the pump and some air will be there too.
Ike