OK. pictures, pictures, pictures.

I think I have an idea what needs to be done, but it will require some changes, and I won't know till I see the pictures requested. But, the info you provided added a question:

+ ? Has the circuit you have ever been used on this pump?
+ ? If not, what are the listed run amps on the motor AND the listed run amps on the previous motor? (One way to answer is simply to include large pictures of both labels.)
+ ? On the 3-wire cable, you say "black is ground". Why is that?
(Blue is NOT a standard color, but is usually a power wire. However the B-W-G colors in a mfg'd cable ARE standard, with black=line (120V), white=common, and green=ground. That is what SHOULD be the case. It is dangerous to leave wiring in another state, because workers or homeowners at a later date are likely to assume that the standard will prevail.)

I just checked your picture again; I can see the black wire now that I look for it. Why in the world would you connect black to ground?

I'm sorry, but you are scaring me a lot with stuff like that. Right now, I'm very reluctant to give you instructions, lest it lead to someone being injured or killed. I have *personally* been nearly killed, twice, by bad do-it-yourself wiring on pools, and twice more (in years past, when I worked a plumber) by fly-by-night electricians or maintenance men cutting corners. One of those occasions was the origin of my hatred of conduit grounding! I also -- myself -- nearly killed a lifeguard, by not thinking through what could go wrong with a vacuum cart I made, even though that cart was 'code-compliant'.

Every body thinks it won't happen to them: I know better.

Is it totally out of the question to hire an electrician?