Atv ran well until it was left out in the rain. The quad has spark and is getting fuel but acts like the combustion is not large enough for it to start.
I have checked the timing and it is correctly set. Has new piston rings, head gasket, and coil. Carb was cleaned again and didn't change anything.
What could it be?

 

Check compression, with a rebuilt top end it should be fairly high but a mistake when putting it together could drop compression.

Rain can affect an engine in two ways, shorting ignition components so you get either no spark or a poor one and, if water gets into fuel tank through the breather, it will find the lowest point, the bottom of the float bowl, blocking the jets. When the "carb was cleaned again" did you check for water in the float bowl?

 

Also may want pull start or do compression check with electric start and then with pull start I think this atv has an limiter on the end of starter and sometime when limiter slips to much it cause the engine not to have enough compression to start

 

Kawasaki ATV 1986 OEM Parts Diagram for STARTER MOTOR/STARTER CLUTCH (E/NO. 0176 | Partzilla.com

 

Photo 39076

 

I did all the listed things after it was left in the rain.
after some thinking and research I am thinking it could be either swapped coil wires or a bad pulse coil. Also there was no water in the gas. I made sure by draining it and putting in fresh gas.