It is rare that the ECU (computer, engine control unit) fails. They are designed to require no resetting, and also, consider this: if you turn the ignition off, the car computer will anyway reset mostly (well, it will keep some parameters in memory, but it is unlikely that those parameters would cause a failure to start). If you really want to reset the computer, you can do that simply by detaching the battery. I don't believe, however, that this would help.
What is the cause, then? Could be anything. No spark could be one possibility. Do cylinders 2, 3, 4, 5 and 6 have spark? You only said that cylinder 1 has spark. No fuel could be another possibility. You said that fuel pump is brand new, but it is in theory possible (although unlikely) that it doesn't work. You need to somehow find out if fuel is injected into the cylinders. Lack of compression or a huge vacuum leak could also cause an inability to start, but there's plenty of redundancy in 6 cylinders so I don't believe lack of compression is the cause. Consider also the possibility that some critical sensor such as the crankshaft position sensor has failed.
In my case, on my 1989 Opel Vectra, I had exactly the same problem. The cause? Bad ECU relay. Occasionally it started, occasionally it didn't, and I diagnosed the ECU relay to be the cause. Replacement solved all problems.