Sounds simple but I bet your connections are dirty, corroded or aren't making a clean connection, my 91 did the same thing. Clean, scrub, sand, etc ALL your grounds and wires on the battery to the starter, ground, and all that. Trust me, they're finicky. Should be a real simple fix if all you did was switch batteries.
If not, you've got the pos and neg cables switched or some ****. Good luck, don't get shocked cause it sucks and keep us posted.
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