1992 Honda Prelude starter

Bought it used. Hhad a short in the ign, switch but fix it. The car will not cranck over. I get a loud snap at the starter. I jump the neutral safety switch. I changed the starter. Battery is new. Iwas able to roll the car in gear for 2 ft and tried to start it and it work(with the key) now i'm back at square 1 with the loud snap the whole car electrical shuts down for about 2 min. This car had an engine swap. It now has an H22 engine the of it. Could the starter be the wrong one. I matched them up side by side and counted teeth. Please help my son is making me crazy