Large capacitor is for the lamp matrix, you can probably get one from great plains electronics (along with a rebuild kit for the power supply if you want).

Besides from replacing the capacitors, the power supply is good if all the voltages coming out of it are correct. There's a diagram in the manual of all the pins and what their readings should be.

Display wise, it could be an issue with the master display board as well.

The main thing that could a damage a new board is bad voltages from the power supply or if one of the switches/lamps/solenoids is shorted.

All those boards get really hot in the lamp matrix area, some blackening is normal and you don't really need to worry about it.

Your pics didn't come through, fyi

They're there now

If those numbers are all you ever got to display then it's normal there's nothing on the other displays. Using the buttons on the coin door you should be able to scroll around and get some other stuff to display. You're probably safe leaving it on for testing since nothing has caught fire yet, but I'd check all the power supply voltages to be extra sure.

My Alien Poker (system 6a) does the same thing if it has no batteries, it shows similar numbers to yours although top left are slightly different as they identify the game. To get past that after you see the numbers open your coin door and then do a rapid power off/on, that should get you past the audit on power up display even if you have no batteries installed. So basically power on, open coin door, then rapid power cycle off/on.

Marco has it.
http://www.marcospecialties.com/pinball-parts/C30KM25VR

Cheaper here.
https://www.tedss.com/36DX303G025BC2A/?gclid=Cj0KCQjw4eXPBRCtARIsADvOjY2Zr1GlDJmCGAn_V1saOZ1rAuiqrHY1ShpsbQdHnAZvsmctk6zH0-EaAhGFEALw_wcB

But this will actually kill 2 birds.

https://pinside.com/pinball/forum/topic/bridge-board-available-for-williams-games

With step by step instructions for firepower. Click the bridge board picture
http://www.pinballrebel.com/pinball/cards/

Make sure the 2 blue screw terminals that go to the big blue capacitor are not touching each other and are not touching anything else, including the floor of the cabinet, when you turn the game on. The big blue capacitor is to filter the power to the lamp matrix. Until you get a replacement, I wouldn't run the machine for long periods of time without it in place. There may be some ill effects to the lamp matrix components from the "dirty" power, I'm not sure. In addition to the options Travish mentioned, you can get one here:
https://www.greatplainselectronics.com/proddetail.asp?prod=CCG-27000uF-25V

If you also need the bracket to mount it to the floor of the cabinet, you can get that here:
https://www.greatplainselectronics.com/proddetail.asp?prod=VR8A

As others have said, the display you are seeing is the result of the backup batteries being dead (missing in your case ). With the coin door open, and machine on, try turning the game off then back on very fast. You can typically get it to start this way without batteries installed.

To answer your question, those boards are in great shape and should be saved. If you end up swapping them all out for aftermarket boards, sell me your old, "junky" ones!

To make the game reliable, you should have those boards reconditioned (new capacitors, header pins, IC sockets, 40 pin connector, maybe MOSFET lamp matrix update, etc) but that should cost 1/2 of what all new boards would run. Reconditioning your old boards will yield a machine that will run for another 30 years.

Not a bad idea, as it solves 2 problems with one part: Replaces the Lamp Matrix caps AND adds fuses to the 2 circuits that are missing protection from the factory.

I've had several of these. It's a great product

27,000 vs 30,000 is not an issue if you decide to go this way. The tolorance of these big caps is +- 20% so technically the 30,000 cap could be any value from 21,000 to 39,000uf. Chances are the 27,000 is right in this range somewhere.