My 99 Mitsubishi eclipse hesitates to stard when cold but after 2 or 3 times trying to start it runs fine

Any tune-up lately, fuel filter.

As long as it runs fine on warm days,
I wil advice u to replace the cold start switch,,...

Don't waste your money troubleshooting. It's The Crank Knock Sensor. Very common issue. Also save the heartache and don't buy a used one as it almost assuredly will be bad also.

sounds like my truck. some security code issue. gonna have to take it to the shop

Check the distributer, or change you plug and its fire, 99 mitsubishi eclipse had a common problem, so i guess this will solve your problem

Probably when you installed new belt you caused the timing to be off and now your camshaft sensor wont allow car to run. 

how old is the battery. may want to replace the battery if is older then 2 years.

Ignition coil my friend

DIFFICULT STARTING CAR IN COLD.WOULD BE A THERMO - TIME SWITCH.THE THERMO TIME SWITCH CONTROLS THE AMOUNT OF TIME THE COLD START VALVE IS HELD OPEN BY MEASURING THE COOLANT TEMPERATURE AND UTILIZING A TIME FUNCTION TO PREVENT AN OVER RICH CONDITION.THIS COULD BE MOST OF YOUR PROBLEM.BUT SCAN IT TO SEE WHAT PCM CODE YOU ARE GETTING.

the heator core has gone out this is a divise that uses hot coolent from the engine to heat the air that blowes tru your vents it is located behind the glove box some times it's tricky to reach look under the hood to find 2 hoses running side by side in to the fire wall on the passenger side to pin point the location