Let's close this one out guys. I wasn't able to get it working and gave up as I dont have the time.
I appreciate all the help.
Incidentally, I sold the computer to a guy who was handy with linux scripts and he said a "short" script would solve this. But again, its beyond my scope and time constraints.
PureOS seemed like a really slick OS too.
Maybe someday.

In T701#13101, @EchedeyLR wrote:

The first error I read it was related with some kernel modules used for the touchpad but I was not sure. Please, run lshw again and dmesg.

That took awhile! But the whole process ran. I rebooted (the computer wouldn't shut down properly) and tried connecting via wifi. No luck. It wont even recognize available networks, which it has done in the past.
Incidentally, the error I've been getting from when I tried installing Linux mint definitely has something to do with the touchpad, but I've tried installing LM with the touchpad turned off and no dice.
So I can't install Mint, but I can install PureOS but can't get the driver for the wifi card.
Hmmmmm. I haven't given up yet.

It's upgrading right now...it's going to take awhile. I'll reboot and try the wifi when the upgrade is complete and I'll let you know.

I have not hit Y yet...

Did not run sudo apt upgrade yet. Here is sudo apt update:

OK...I checked for updates and it said the system was up to date. If you know how to manually update the kernel via the terminal, please let me know and I'll run the commands.
As far as the dmesg command, it returned an insanely long string where every line was the same:

I have no idea how to run as a superuser but it did give me a warning that the data may be incomplete unless I run the command as a superuser

Per your request.

Please, make lspci on a terminal and post the output here.