Well I managed to upgrade the laptop to Windows 8.1, then I used a how-to thread in the TenForums to create a bootable USB with a program called Rufus. I could not get the USB drive to appear as a bootable option in the BIOS, or in the quick boot menu upon startup (F10), so I just clicked on setup.exe from the USB drive once I was on the desktop.
It appears to be updating to Windows 10 without any issues so far, but we'll see. Maybe using Rufus made the difference.