IT WORKED IT WORKED IT WORKED!!!!!
I was able to start my old laptop this morning and grab all the most important client files off it!
Of course, as I was pulling other files I heard periodic odd sounds (a kind of scraping, white noise, maybe sizzling sound), so I thought to pull my power cord out and just let the battery carry it.
OOPS! Bad move...The computer immediately went black...
Ahh, but I tried turning it on again later and was able to get all the rest of the files off - YAYYYY!!!
So it looks like I've gotten everything (perhaps with the exception of some stray files or preferences that are in odd locations and that I don't realize I am missing, but I will attempt a TimeMachine backup to grab those in case I ever go searching for them) My old laptop is unreliable (goes black when the plug is pulled) but perhaps I can tinker with it and find a use for it.
Regardless, this is me right now:
@jimsz Thanks again for the recommendation to simply keep my active files in my Dropbox synced folders. I moved them into there!
Again, I posted all this in hopes that it might be a reminder to anyone else here that may have not backed up lately or might have been keeping open liquid containers nearby.
Back-up often and keep liquids away!