Just bought a 1982 200ES Big Red, the battery was totally shot so I put in a new one. It starts great with the recoil but absolutly nothing with the starter.

Any tips on where to start looking for the fix?

 

first off it is an "E" the "ES" was an 84. you might take the starter switch off and see if it is coroded or have the starter tested.

 

Check the continuity at the button to see if it is good. I had to take mine apart and clean it out/sand the connections then it worked fine. If the button is fine then you have to check for power at the starter motor. There are a few other things, but its been awhile. There is a list of things in the manual.