Car have problem starting

I Just did a major repair on my car, it all started with car will not start at all. It was a bad starter. I replaced the starter and adjusted ignition timing for smog. Two days later car broke down on the freeway and the radiator cracked due to excessive pressure. This time it was timing belt failure. I replaced timing belt, water pump and radiator and thermostat and all hoses. I paid over $900.00 for the job. Next day after I picked my car, when I was taking my car back from lunch car would not start again. Battery is on, starter is working engine is crank and make grr grr sounds then does not start. I tried a couple of times and finally it worked. Later I notice it only does that when you turn the key have way (ideal or ignition switch) and leave it for a couple seconds after that it will not start. If you take the key out and turn immediately it will start fine. Battery is three months old, sparks are new, all other possible connection is fine. Not sure what is the problem.