Welcome to Pinside!
Don't leave the machine on in this state. You'll blow a fuse, burn up the coil or start a fire.
Since you said the switch isn't stuck closed the next suspect is a bad driver transistor. I looked in the manual but it doesn't list the driver transistor on page 16 of the pdf available from IPDB.org. It will be in the schematics somewhere.

Pinwiki can give you some guidance on testing transistors.

First double check that the 2 large connectors that go between the body and the head are correct in that each wire is the same color on each side of the connector. Do *NOT* depend on the color of the connector (white/natural, black) means it's the 'correct' one. Look at the wire colors themselves. WMS was sloppy around this era and sometimes used different colored connectors (instead of black-black, it could be white-white, white-black, black-white).

Hopefully you do NOT have this issue (you likely don't since it's coming up with 2500 4 on the displays) - one of the symptoms of that mismatch is that the flippers lock on (also probably not because both flippers lock on, and the game will not boot) - in that case, all your +5 chip received solenoid voltage and lots of them would probably be blown.

You're going into audit mode (2500='2'=williams blue roms, 500=game # (black knight) and '4' is the software revision - 4 is the latest official) and then the game is advancing through all the audits to 50 (that's the counting # at the bottom), at 50 the game resets itself and goes back in.

Looks like your advance button on the coin door is stuck as that is the behavior that would happen in this situation. Disconnect the coin door and see if the behavior changes. There are 2 connectors at the top of the mpu board that are 4 pins that sometimes get swapped and it might be one of those.

There is no transistor that controls the left flipper. There is a transistor that turns on the flipper relay, and if the flipper button is on, so will the flipper go up. Since the audit/adjustment mode also turns on the flipper relay, that flipper being up is a separate issue.

On YouTube joes classic arcades, there is a recent set of videos about black knight
He has a machine he believes had the connectors plugged in incorrectly at some
Point. In one of the videos he goes through all the things that could be damaged. It can be allot unfortunately.
Might be worth watching

If you have caps across your flipper switches clip those as they can short essentially bridging the cabinet switch. One way or another you've got a closure there at the cabinet button. if memory serves they are directly powered thru the cabinet switches. No transistor. The flipper enable relay being on on bootup is something else. But maybe there is a plug a pin off or something causing a bypass situation

Wait a minute I read some more posts.... Did you mix up the black connector and the white connector in the backbox? If so stuff blew up my friend.

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https://www.pinballlife.com/rottendog-boards.html