I've seen that issue with the keyboard before, i have 1 or 2 keyboards that will not work with these units, sometimes more exotic keyboards don't work, with lots of multimedia functions.
There is no "drop in replacement motherboard". You buy another original theatrythm TTX3 unit that works and that's about it. Try a wanted ad on here? But you'll need to specify that it has to be an original FF game and it has to be working with original HDD, not converted to multi. Unfortuantely due to multi availability, the price might be higher... Or wait for one from Japan to pop up. I don't see FF theatrythm units that often lately, but they are generally cheaper because the lower specs just make it more expensive to multi.
Don't feel too noob, it sounds like the board is defintely not working in some way and you've troubleshot to the point where you can't do much more. They aren't that special in that it's super hard to get them to boot, they should just boot fine easily with the original hardware, at least to the splash screen. Given that it was starting to fail on boot ups before, it's a good sign something was going bad. You can boot and run the unit on the onboard video so you know it's working at least, this kind of rules out all the other troubleshooting stuff that you would normally try because the board boots with onboard.....and runs fine.
I think you are right about the pcie slot having something wrong with it, or someting on the MB around that. Not really much you can do there, it happens... they do go bad unforutnately. So you're at the point now where you just call it a dead board in some way. You could start trying other video cards, just for the hell of it but that'll just cost you $$ and you need non UEFI cards.
So your options as i see it.
1. Buy a new TTX3 FFT board and plug it in and away you go. (You could send
@Cereth a message on here, he is US based and he might have a spare, but he is really busy and i'm not sure if he would have a spare unit laying around for this game). There's some value in your current (partially working) ttx3 unit. Not as much as a fully working one, but still some value in the whole unit. If you buy a replacement TTX3, you can just sell the old one to make up some of the $$.
2. You could try and update the bios on the motherboard to b23 to see if that helps in any way, be warned this is really a 1 way bios flash and if it does make the unit work again, your original game may no longer boot anymore, so you are back to option 1, and you will need to install windows on a HDD to get the unit to boot Windows instead of the original hdd (more tedious work for you). I don't see why it won't make the original game boot, but i just can't say it won't as it's uncharted territory and i'm not sure how fussy the original is. I don't think this will fix it, it's just something you can try, given that the unit is basically sort of dead anyways.
3. You could try to make the game dump run on another machine, but this is the long drawn out option... and again, you're in uncharted territory for me. The game will boot fine on other pc's, i just tried it, but will it talk to your original IO board and hardware? who knows, you'll also need to swap the dMAC out of the original unit to do this... I'd say skip this option.
Option 1 is the easiest and i recommend you just do that. Try Cereth, but don't hassle him with troubleshooting requests, he's a good guy, just super super busy, but ask him if he has a working TTX3 FFT unit spare and you might be in luck. Or just request on here, and keep an eye on YHJ.