Need a new water pump

First, be SURE there is no air leak on the suction side at any of the fittings. I would think that since you have the same issue at the 'winterizing port' that the trouble lies between there and the pump (or in the pump). That said, I had a similar problem and decided that since it wasn't working, I wouldn't lose anything by taking it apart so I carted the pump into the house to the kitchen table. What I found after carefully dismantling it was that the check valve on the input side of the pump was mechanically stuck in a slightly open position. Touching it instantly freed it although I could not see why it had stuck. The clearances on the valves were very close and my assumption is that a tiny speck of something too small for my ancient eyes to see got stuck in the valve. I rinsed the valve body in the sink, reassembled it and it has worked fine for a year now.