16.5 hp briggs, new battery and starter, starter spins but does not engage. 2 of the copper wire coils under the flywheel gets hot and the wires going to it

Make sure you have the battery right ,sounds like you have the cables on the wrong side,

Try DG's suggestion. If that is not your issue then you might remove the starter and take a look at the starter bendix. When the starter spins the shaft spins and a nylon gear should slide down the shaft as it spins. This gears enagages with the flywheel but if the gear or the shaft aren't working the engine won't turn over

WOW that's embarrising I should know better than that, I did, new battery was reversed of the old one, just put the fly wheel on mower fires up. Thanks DG

DG spotted something that never dawned on me. Batteries can have posts reversed but appear the same. Always us the same product # and watch for the letter R in the product #. Maybe stop by and give DG a positive check mark, I did.