There are some things that are pretty evident from the video, and one that isn't. And that one could be a huge one.
The score reels are not resetting. As long as they don't reset to zero, the game will never start correctly. In the backbox there is a relay that has the job of pulsing all the score reel relays (also in the backbox) and resetting them to zero. Once they're are at zero, the zero position switch on each reel will open, which tells the game that all reels are at zero. At that point, I think the game relay, if I recall correctly, will change states (it's a latch/trip relay) and then the ball will be sent up to the shooter lane. Also, the ball count unit needs to step the balls to play unit to three or five, depending on what you have it set on.
You can try and work the reset relay by hand and see if it moves the reels at all. You can also just reset all the reels to zero and see what happens. But as long as the reels are not all at zero, the score motor will run on forever.
That fuse hack needs to be corrected. You need to get a schematic and make sure all the fuses in the game are correct.
Now, on to the big one. It might be nothing, in which case you can eventually get the game working. Or it might be something, in which case you are pretty much screwed and it's going to be extremely difficult to get the game working.
On the motor board on the bottom of the game, you see that long plastic piece with teeth on it, look almost like shark teeth. ? It's on that long row of relays on the left hand side of the board. That is the trip bank for the numbers on the game, the tilt, several other different relays on there. That entire bank has to be reset at startup, or the game will not work. And it is reset by a motor turning that long piece of plastic with the teeth on it. It resets them in sort of a ripple fashion by the motor turning that long piece of plastic, and the teeth making contact with the relays and forcing them into the reset position. In your video, it's not turning as the score motor is running. It has to turn. If it doesn't, the game won't work. There may be several things at work here. It could be that power isn't getting to the motor. If so, you have to figure out why. It could be that power is getting there but the motor is bad. Worst of all, that plastic tube might be broken. It has been known to happen. If that piece is broken, you're in bad shape, because that piece is not available anywhere except for a donor machine, and you'll have to have either the ability to find a replacement piece, and have the ability to replace it, or you'll have to find someone who can.
I hate to be the bearer of possibly very bad news, but I owned O&E at one time, and if that reset is broken, you've got a mess on your hands.