1996 2.4L check engine light when cold

car's check engine light comes on when it is cold, goes off when the temp outside warms up. live in michigan, so we're talking teens when cold and forties when warmer. new plugs, coils and distributor cap. shakes also when idling and wouldn't start for me yesterday. sun came out for a few hours, started right up. checked battery and that's good too. any ideas?

How many miles on the car? and When you say it will not start, does the engine crank over like it wants to start?

I had the same problem with a 94, and it was the ignition module. If you start to smell like wires burning then that may be what it is.