Sorry to hear William that you are going to have to replace the under felt.
I guess the shop vac can be used to evacuate the moisture for now though.
Is there no way to save it or has it completely falling apart?
I have seen on ebay some under pad and you can google "Auto Car Carpet Underlay Underpad Felt" and see what you come up with for your area.
Alternately carpet shops may have felt pads available, or a local trim shop should be able to help you source the right pad and thickness.
I know if I was to remove my front seats it would be a bit of a struggle, and I don't have all data to see a diagram of your mounts/electrical.
I hope one of our members has removed the seats on a 1996 PA before to be able to help you better.
Normally though it is like you said pretty straight forward. I would disconnect the battery before removing electrical connectors, and find those bolts, and with a grunt lift em..LOL..
It may be best to have an extra person to manage them out of of the front doors. I can see that may be a bit exciting & you dont want rush to damage the seats pulling them out.
I wish we lived closer I would give you a hand.

When I lifted the carpet, and removed the pad it was soaked, and falling apart pretty badly, there was a good 3/4" of water puddled in the middle, so it will have to be replaced with something.
My main concern is finding that leak, so I'll get a hose and hose the doors down, and see if I can see any water coming in around the rear door area, if I do then I may be able to put some padding down in the rear, and put the carpet back down, then shampoo it, that would save me from having to remove the seats.
My main worry with removing the seats is the bolts possibly being rusted, if the water kept wicking its way towards the front, or if somehow the water is coming in from the front, but just somehow not getting the front floorboards wet, then they could be rusted.
If I can get it out I think I can get them out by myself, not that I have a choice, one way or another I'd get it done..

I found something that looks like what was under there, I am sure it could be cut to fit, of course nothing is going to fit as well as the factory stuff.
Auto Car Truck Carpet Underlay Underpad Felt 36" Wide 40 oz 7 16" Thick Yard | eBay

I hope the leak is not coming from the front cowl where the wipers are, I have heard of some cars taking water in through that area, that would be a nightmare to track down, I read about one person that had to remove almost all of their dash trying to chase a leak down...

the seats on almost all the buicks are pretty easy. 2 bolts in the rear, move the seat so its over the track'* footprint after you undo those bolts, then you tip the seat forward then pull up/back. there is an L shaped hook that goes into the floor, thats why you need to tilt forward then pull up/back.

as for the rust issue, i wouldnt worry. just make sure you have the right size torx bit, or a 6 point socket if you just have hex heads. you have to remember, the seats are what hold you in in the event of a crash. they use grade 10 bolts. also, those bolts go straight thru the floor. when they are removed, you will see the ground underneath the car thru the holes. regardless of the moisture IN the car, they have been exposed to the elements at the other end since 1996. they wont use cheap bolts on something that is that important to safety.

Thanks Jason, sounds like it should not be too bad.
I just need to wait till I have some money to spend to get the insulation stuff for under the carpet, as well as the money to fix the leak if I can track it down.

After dying the back passenger side floorboard up I waited for it to rain again, went out and took pics, at first it looked like it was coming from the rear floor board/door area somehow, and that made me happy for a minute, till I popped off the driver side kick panel trim, and I seen that water is coming in from the front somewhere, probably from the wiper/cowl area, which was what I was hoping was not the case, but since the front floorboard on the driver side is wet along that right side of it (if you are sitting in the seat that is), I really have no choice but to take the seats out, remove all of the carpet, and try to find the leak, which I have a feeling may not be possible without half of the dash coming out, I seen where somebody on an older Buick had a similar problem, and that is what they had to do, and in the end they still had trouble sealing the leak once they found it.
Being that it is my only car, and money is still pretty low, I don't want to go pulling the seats out, and not being able to afford to fix the leak, whatever may be causing it, unless it is as simple as using a little silicone, provided I can even track the leak down..

The pic is of the rear floorboard, the water is flowing down that channel up under that trim, coming from the front somewhere, and following that channel to the back.

Not good William. I take it it is only coming in from the drivers side area. It is at all wet under steering column area? Could it also come from windshield, down from A pillar possibly ?Ya I had I similar leak on the Cutlass before. I had to pull the driver'* side fender to find the leak..fun..Not. Puling the dash even less fun.
This is what I did, and it was winter, so I knew what ever was going to happen would be a while, until I could work on it spring/summer time frame.
I made relief cuts into carpet to peel it back, did not remove front seat.
Bare metal now..all around driver'* foot well. Large thicker towel on floor & then regular all season mat on top of towel. Had to change the towel every other day depending on rain etc. Always had a spare dry towel to replace it with. Water kept in front and when it got sunny / warmer in spring, then I did the 9 yards to find/fix the leak & repair carpet properly.
Gm has a body seam sealer that is really good stuff. I would not use silicone.
It wont hold up in the long run.

It seems to only be coming in on the front passengers side, and making its way to the rear due to the small incline where I park.
I'll look into some seam body sealer if I can ever pinpoint the leak.
If I cannot find/fix it before rainy season comes back around, I'll be forced to get a tarp, and hope I don't scratch up my paint, it is due to be repainted anyway..
Scratched paint is better than rusted metal, and mildew growing on my steering wheel.

Well, I removed the trim from around the passenger side kick panels, and pulled up the font carpet enough to see that the whole front passenger side floor board was wet, as I figured it was.
Also it seems like the water may be coming in from the firewall area somewhere, and I think it is coming in the center of the front, around the hump area.
Worst case scenario seems likely now, looks like I am going to have to remove the wipers, and the cowl guards or whatever you call them, and see if I can find a clog somewhere, or an area that is letting the water in.
Not doing that till I can get a tarp, I don't want to let more water in, I need the area to dry up a bit, then I may sprinkle a little powder around the area, and hose it down to see if I can find the area of the leak.
I did find my ground buss though, on my 96' PA it is on the passenger side, as soon as I pulled the carpet back I seen it, so at least I know where that is in case I ever have any ground issues..

William are you just going to cover the front with a tarp or the whole car?
I hope you can find that leak. I know it is a real PITA to fix water leaks in general, but I have confidence you will locate it.
How does the ground buss look, any corrosion so far?

I am going to have to cover most of the whole car with it, at least down to the wheel wells, if not water will fond a way to get to that cowl area.
The ground buss was up above the area where water could get to it, and it was wrapped up good, so I did not bother to unwrap it, it is easy to get to so if I ever have a problem I can get to it with ease.
So far all of my electrical works well, except for an occasional short from my headlight switch, if I use the twilight sentinel to make them come on they work fine, but if I use the headlight switch then I get a buzzing sound coming from the chime speaker, it is something I need to get fixed as well, but I can only handle one problem at a time, I rarely drive at night, so it is lower on my priority list than the water leak.