The best way is to be methodical, patient, and logical. Use a solid understanding of how the machine works combined with analysis of the schematic to attack problems one at a time, and you can get it working. The schematics can seem very complex and intimidating, but in the end they are actually logical once you understand them, and even though they are big it is really can be broken down to a bunch of smaller circuits with various jobs.
You can try out my thread here to get some background of how the schematic works. It turns out that this Space Time is a similar vintage Bally machine, so even though they aren't exactly the same, the schematics are very similar in many ways. Many of the concepts in this thread will apply to your machine.
It is best to take things one at a time. The first thing to deal with is this: something is off with the startup sequence. Let's see if we can figure it out. The schematic is online at the pinball database so I have it. Next we have to get the problem(s) defined so that we can understand everything, then attack it. You have to get the startup sequence working correctly first and then go from there.
Are you putting coins in to get credits, or has this been modded for free play?
Either way, when you press the credit button, these things should happen:
- The score reels reset to zero.(If they are all at zero, manually advance a few of the reels to some random number so you can check this. If you don't know how to manually advance the score reels, check back for advice).
- The total play meter will advance by one (you have to observe it underneath through the open coin door).
- The ball count unit will reset, so you will be on ball one.
- The player up unit will reset so you will be on player one.
- The game over relay is energized, so the game over light should go off.
- The ball will be kicked from the outhole.
You already said the ball is not kicked out at the end. Do all of the other actions work as they should? These are all tripped by the score motor, so the score motor should be going through a cycle or two while this all happens, then stop.