A drive not showing in windows is a beautiful addition of new UEFI Bios's. There's a setting in there to choose AHCI or ATA. Sometimes other selections as well, such as IDE or Auto. If your drive is set up to work as a IDE drive due to its' age and you're moving it to a new 8.1 system with newer HDD options, BIOS will recognize the disk. It will tell you it's there. But if the correct setting isn't selected, that's all it will do. Recognize it. It won't load it. Sadly... Newer tech isn't always going to make things easy.
If you change this setting, your boot drive might not load. Then again, it might. Part of the risk here is the BIOS writing to the drive to tell it that it's booting with a different driver from BIOS. The boot drive might not support that mode. Then when you change back it might fail to successfully accept the driver it's always used. Not guaranteed to go down like that, but possible.
Your best bet is to get a USB Dock to throw the old drive in. Plug the drive in, boot windows, then plug the dock into windows. Since it's USB it loads off the USB drivers that were loaded when you first plugged your computer in and is now a PNP device. Should work like a charm.
Alternative options are to use another OS. Windows can be finicky. A linux Live CD might allow you to have both drives plugged in and it might load both drives without having to screw around in BIOS at all.
Also, some BIOS's have options to enable specific SATA ports (if this is a sata drive and not an IDE drive, idk how old this drive is). Could be the BIOS is showing you there's something connected to the port but it's not initializing it due to the port being turned off. Or something similar going on.
Hope this helps.