Overheating

Got into an accident and had work done to replace radiator, cooling fans, AC condenser, got the car back and it over-heated. Mechanics did not check the coolant if it was transferring or not and it was not. It ended up blowing head gasket and the shop replaced engine at no cost to me as it was their fault for not double checking. All, was good until two days after went to start my car and it didn't start it sounded like it wanted to, but did not want to kick over. Engine light came on and diagnostics came out just for an oxygen sensor. Which I do not think will cause to miss-fire. So, at work we have mechanics and they just opened up fuse box and checked fuses and everything looked fine and than went to start car and it started up. Could it be wires loose/maybe fuel intake causing this delay? I am taking it back to shop where repairs were done, but just want to make sure they don't try and screw me over as this is the third time going back.