So on your schematic you'll see the various switches that cause the score motor to run: W, E, I, O, S, SB, and one at motor position 1C (these are just the ones in parallel, ignoring the reset path that also causes it to run via a DB2 switch).
The only two that are related to scoring/game play are E and I. W, O, S, and SB are usually all on the score motor board, so are near the score motor. But where are E and I located? The path from I apparently is working, since manually activating I does cause the score motor to run. But the path from E to the score motor might be suspect.
Otherwise, the E and I relays don't have very much in common, so it might be better to debug one at time for now.
E should energize whenever either "Single" rollover switch closes. E should stay energized ("locked on") via its own switch, and a normally closed switch at motor position 2B. But a switch closing on E when it energizes should also cause the score motor to run (which in turn will de-activate E when the switch at position motor 2B does open).
It won't score the 100 points either without the score motor running, since it needs the first pulse of the score motor to do so.
I think the simplest thing to do would be to focus on the switch on E that is supposed to cause the score motor to run, and the path from there to the score motor. Looks like one side of that switch is going to be with a GR+RED wire.
Now, the I relay is a different path. The I relay is directly energized via the three top rollovers switches, or the two "2" standup targets switches. Once energized, the I relay should stay locked on via its own switch and until a switch at score motor 2B opens. If none of those five playfield switches energizes the I relay, then it's either the I relay coil, or there's a common open in the path.
Since the I relay has a lock-on path, if you manually activate I and it locks on and holds while the score motor runs, then the coil is fine. That then means there's a common open in the path. If that's the case, then the thing to consider is where is the I relay located relative to the playfield switches? If the I relay is on the score motor board, or is in the backbox, then there's at least a Jones plug involved.
So in both cases, it could be as simple as a Jones plug possibly, depending on where E and I are located.