Status update:
Not really sure what's going on with my 2nd desktop PC regarding the update. Checked Windows Update again, and it said it had a failed install. Looking into the history, it was attempting to install Windows 10 Pro (roughly 5 times now), and the order of which the errors came from them were as follows...
80240020 - 3 times - Windows 10 installation folder is unfinished and/or corrupted. Follow steps to delete stuff in SoftwareDistribution\Download folder, run "wuauclt.exe /updatenow" under admin command prompt, and go back into Windows Update - did it, but no redownloading
80246007 - 1 time - Change or restart the Background Intelligent Transfer Service (BITS) - did, but still had problems
80010108 - 1 time - Run the System Update Readiness Tool - currently downloading
While I'm in the process of downloading this tool, I kept searching around for answers, and I got this message on Microsoft's website (not a pop-up, but it did some out of nowhere)
-------------
July 29, 2015 - Where's my upgrade? It's coming!
With your reservation, you are in the queue for your upgrade. Watch for your notification to arrive in the coming days or weeks. At that point, you can upgrade immediately or pick a time that works for you.
------------
So they are going off a queue, and I just have to wait? It's odd that I've had all these problems because it wanted to do it automatically, yet they tell me this? Maybe I'm "back in the queue" after the failed installation.....
My laptop, however, seems to finally be doing something after doing the step above regarding error code 80240020.