92 Ford Club Wagon XLT no hot start

92 ford Club wagon XLT, 200 000 miles. When cold, it starts right up. After It has been driven, if I turn it off, the engine turns over slowly, for a second then stops almost as if it had a dead or dying battery. But if I let it sit for at least forty-five minutes, it turns over and starts fine.

I just bought it, and the prior owner tells me that he has changed the battery, alternator, and solenoid while trying to fix the problem. He included a new starter with it, and I have put it in. The battery cable connections both positive and negative appear tight at both ends, though the negative termina clamp was broken, so I just changed it tonight.

Other than having the battery load tested, I am not sure how to procede in troubleshooting this.