A bargain, I didn’t think it was possible to get a top end Williams (in terms of gameplay) for that price any more.
Ok, so if we look at this logically, the game was switched off 5 years ago because it had problems and the owner couldn't or didn't know how to.
5 years it switched off in a cold place, in my opinion electronics especially temperamental ones like STTNG are bound to develop some sort of problem with the various bits on the boards. From experience I believe mine was stored for a long while and it had problems, some caused by me, others from age, others always there, like the fliptronics board.
It's pretty easy to put the ribbon cables back in wrong, I know I have done it, check these first.
I have personally heard it’s not uncommon for Rottendog boards to come faulty with some soldering needed, its possible your replacement fliptronnic board is one of those.
As you don't have any board experience (me neither, so nothing wrong with that

) I would eliminate these first, you will always be chasing your tail and scratching your head, the other bits are easier to troubleshoot.
1) Get a new ribbon cable
2) get the boards checked by someone. Phil at Pinball heaven is very helpful and should be able to help or Pinball mania, who I believe specialise in Williams games. Both companies are trusted and well respected. Alternatively post a new thread, need fliptronics Williams board, (I would use the original one), Rotten dog CPU board and Williams Power driver board checked. There’s bound to be something wrong with one of them. Even if there isn't it will make it so much easier to troubleshoot as you will then know 100% it’s not the boards
3) before re-fitting the boards check that the diodes on the all the coils are all in the right direction, triple check this. Make sure the banding is the right way round. Check on this forum people will help. If you don't and you plug the boards in, and one has been fitted incorrectly you will damage one of the boards.
I think your wasting your time troubleshooting further until the boards are eliminated. My hunch is there is a problem with one of them, fliptronnics originally and maybe now the CPU, display driver or powerdriver board or all of them
Other more experienced members might disagree and be able to point you in the correct direction, however the reality is, like myself, you have no board experience, you don't want to touch boards so can't eleminate these from the issues.
Unitl you do, you will never get it fixed
I’ll give you £1,300 for it

(don't take my offer keep it and preserve you will get there)
This machine will not be fixed quickly, without putting the hours in, be patient and the reward will come of it working and being able to play it and know that you only paid £1200 for it in 2021! That you can def gloat about (when its working!)