I found out why the Windows 7 installation DVD wasn't booting correctly...
I'd noticed that one of the USB devices I'd plugged in -- when initially trying to find out which one was my keyboard -- was my Xbox controller. After unplugging this device on the supposed "crashed" screen of the Windows 7 installation, all the correct prompts popped up, and allowed me to go ahead with installing Windows. So, I made sure I only had the bare necessities plugged in, restarted (just to be safe), booted into the Windows 7 installation DVD again, and have now successfully installed Windows 7.
At this point, I couldn't get on the net to download anything, as none of the components were supported by my Windows 7 installation, being that it's 6 years old. So, I installed the Gigabyte drivers and utilities using the disc that came with the motherboard, got on the net, navigated to the "Get Windows 10" page on Microsoft.com, upgraded to Windows 10, burned the ISO of Windows 10 onto a blank DVD using Media Creation Tool, restarted, booted into the Windows 10 installation DVD, deleted all existing partitions, created a new partition, installed Windows 10, reinstalled the Gigabyte drivers and utilities, and now everything seems to be working OK. Well, except whenever I open specific installed Gigabyte utilities, and then I'm greeted with the not-very-helpful error message; "This driver can't release to failure!!", which I haven't yet been able to find a solution for. However, they still seem to work.
An interesting discovery with the BIOS...
When I *did* manage to access the BIOS, I turned off the "Show Logo Screen" option, in the hope I'd be presented with a proper POST screen, as opposed to the Gigabyte splash screen logo, but I didn't get to see the POST screen I would have liked -- instead just one with the "American Megatrends" logo, and the option to press either DEL or F2 to enter the BIOS -- but for some reason, with the Gigabyte splash screen logo disabled, I can now access the BIOS every time.