Three thoughts after reading through:
1. Regarding setting jumpers on the old IDE drive, I'm sure you should set it to Master (or, Master with No Slave Present, if that's an option). ANY IDE port MUST have a Master device on the port to work. The adapter you have creates an IDE port from a SATA port, so it must have a Master.
2. Power was mentioned. Any IDE HDD needs two connections to it: a 40-pin data connector and a 4-pin Molex power supply from the PSU. The adapter you got provides the data connection. But you must also provide the power connection. Maybe you are expected to provide it yourself by using a 4-pin Molex output from the PSU (it's about ¾" wide with four holes in a straight line), or maybe the adapter came with a small cable to help do this. If you provide details of th adapter you're using we might advise further.
3. Formatting is NOT your problem. If you Format that old drive, you will lose ALL your data! Fortunately, you can't do that right now because your computer does not even "see" the drive, so Windows can't manipulate it. It would be possible in Disk Management to Format it or to Partition it, but either process will destroy old data, so don't do that! I have no doubt that Win 8.1 has a "built-in" driver for IDE (PATA) devices, AND that it knows how to read any such drive that was Partitioned using the old MBR system and Formatted with ANY of Windows' Format systems.
As has been suggested, maybe the adapter you have is faulty. Another possibility comes from the question: just how old is this HDD? Up to mid-to-late 1990's there were IDE drives that did NOT use the current LBA access system. To install and use them you had to set in BIOS Setup at least three parameters for the drive according to the label on it: Cylinders, Heads, and Sectors. Sometimes there also were Landing Zone and another. Does the label on the drive show this info? Can you post the exact maker name and model number of that old HDD?