You don't need a compression tester. All six didn't go bad at once and you can run on 3 cylinders. (Don't ask). If you have spark and fuel, then it's going to start. If your headgasket was bad..you'd still start and then it would run badly.
Maybe a crank sensor or icm. Any codes at all? What do the plugs look like? I've had issues starting in the past if the car was key clicked a bunch of times before firing up. It's because each time you click, you prime the cylinders. Too much and you soak the plugs. Wet plugs don't fire.
