Pool pump problem

Just some general advice: Check/redo the wiring connections. There are silicone filled wire nuts available if corrosion in the motor junction box might be an issue. The wire nuts are made for underground wire splicing. Ace Hardware should have some. Loosen and retighten any other wiring connections leading to the pump.

So, the pump is the only load on that GFI? GFI is a breaker type?

First I'd disconnect the wires at the load side of GFCI, see if it will reset and hold. If it does, then I'd probably disconnect the wires at the pump, reconnect the wires at the GFCI and see if it holds. If it does, then you know it's the pump. Water in the pump doesn't sound good. Where is the pump, outdoors? Typical pool pump is designed to be out in the rain without water getting in. And if water does get in, probably hard to get it out with just a heat fan or similar.

We've gotten something like 5 inches of rain over less than a week. Normal rain, doesn't cause any problems. All else was tried, thanks anyway.