When you moved the IDE hard drive to the old computer, did you make sure the jumpers were set up properly? Any IDE port and cable can handle up to two devices (well, assuming the ribbon data cable you have has a middle connector for the second device). Any IDE port MUST have one device (usually the one on the END of the ribbon cable) set as Master. IF there is a second device, it MUST be set to Slave. This is done with jumpers on pins on the back edge of the drive, between the 4-pin power connector and the 40-pin data connector. If there was a Master there before and it is the ONLY device on the cable, check for a subtle difference on some drives. Some make a distinction in the way to set jumpers between Master with No Slave, and Master with Slave Present.
Now, if instead you connected the second HDD in the old machine to a SEPARATE IDE port and cable so it becomes the only device on that second port, then it MUST be set as the Master of that IDE port. And the settings of devices on the other port (which you are not changing) must be left as they were.
If you got all those right and the older computer still cannot read the HDD you moved, it's a strong indication that the HDD itself may be faulty. Maybe that's why it was misbehaving in the original machine.