Alright first C18 shouldn't have a connector so that's normal
Your burnt J5 is probably the reason why you don't have all your lights. That connector is what powers all the lights that are out in your game. When you get new fuses or a circuit breaker (more on that later) keep J5 unplugged and start up your game if the flippers work and nothing blows then it's definitely that connector. With J5 unplugged you should lose the GI lights but the game should work like normal.
Unrelated to the connector but sometimes the coin door switches need to be pushed in or pulled out for the flippers ball eject and the rest of the coils to work. It's a safety put into the games so when you have the coin door open you don't shock yourself by accident. Theres been times I was fixing my game and I forgot to push or pull out the switch and the game will start but no flippers or ball eject.
Your videos were pretty good but I personally wouldn't be able to tell if all your connections on the top row are on the right spots especially the ribbon cables. Though they are facing the right way cause the red line faces the right side of the game when looking at it.
Here's a few things you might want to invest in
First is a NVRAM extremely easy to install on Royal Rumble just unplug one chip and put in this one. This will eliminate the need for the 3 double A batteries. It'll save your scores and settings. And won't leak battery acid on your board. There are cheaper places to get them but pintech will make sure you get the correct and best one for your game.
Also if you plan on getting more pins (or even if you don't) look at getting a few different rated ones of these circuit breakers. Great for chasing shorts you won't need to keep wasting fuses. Just push (or twist) and they reset.
They are just for testing though. Once you fix the Short you can go back to a regular fuse.
Also greatplainselectronics.com is a great web site for buying a new J5 connector, pins and fuses.
Lastly this one isn't a necessity like the other 2 but more of a shameless plug. A color screen DMD looks really nice. Heard the guy that colored it is awesome as well
Hope this helps.