My CRX would shut off while in 2nd and/or 3rd gear for no reason...Took to shop they said my distributor was bad...Replaced it and it ran ok with hesitations and surging while driving...One day car would crank but won't start and check engine light is on...Replaced main relay but that doesn't seem to be the problem...No ECU codes either...Any ideas????

 

Not enough info. (Si, DX, or HF?; no codes makes it tough)

-when you turn the ignition to ON, does the check engine light come on then go out in two seconds?

Try
-Resetting the ECU (disconnect the negative battery clamp for 15 minutes).
-check all the grounds (main body ground, transmission ground, thermostat ground, and the grounds to the valve cover)(bad ground can cause all kinds of problems because sensors that the ECU runs everything off give bad data)
-clean your battery connections
-check all fuses
-check the vacuum lines (the one to the MAP sensor is critical; surging/hesitations could be caused by vacuum leaks)
-when was the last time you did a tune-up (new air filter, pulled and gapped the spark plugs, adjust the valve clearances, check/set the timing to spec., changed the oil)?

Other things to check:
-how many miles does the fuel filter have on it?
-the electrical part of the key ignition could be part of the problem
-check the sync between the cam and crank shafts
-set to TDC on compression stroke of cylinder #1
-look at cam pulley (two lines should be parallel to head surface, and a third should point down to a witness mark on plastic shroud)