Let's make sure you "checked the jumpers" correctly - and maybe you did already! Since you have 2 IDE drives, I'll start by assuming they both are on one ribbon data cable. IDE drives ALWAYS have to have some Master or Slave identification because the port will handle 2 drives on one cable. With both on one cable, one should be jumpered to Master (sometimes there's a separate setting for Master with Slave present), and the other to Slave. Note that this has NOTHING to do with the boot drive (boot drive is set in Bios Boot Sequence Priority) - it is just the identifier on the shared cable. The alternative is to set BOTH drives to CS (Cable Select) and let the ribbon cable take care of it. Then make sure the Master is the one at the END of the cable, and the Slave is in the middle.
How is your CD or DVD drive connected? If it is also an IDE device, it should probably be the Slave on one of the IDE ports (probably Port 0), with one of your IDE HDD units as that port's Master. That would require connecting the second IDE drive as Master on the other IDE port. In fact, this MIGHT be part of your trouble. Some CD drives can handle being the Master on an IDE port if it is the ONLY device on that port/cable, but are not "smart" enough to be Master with a second device on the cable. In that case it is important to make the HDD the Master on this two-device IDE port/cable, and make the CD drive the Slave.
When you tried out the second IDE drive in an external enclosure, you would have needed to change the jumper. An external enclosure only holds one IDE drive (usually) so it MUST be the Master - an IDE port can't operate without a Master. So, during your tests, did you set the drive that way? And, did you change it back when returning it to the computer case?
By the way, if you have two IDE ports in your machine and the two drives are connected separately to the ports so that each is the only drive on its cable, then BOTH must be Masters - one for each port - and each should be plugged into the END connector if the cable has two.
If all that is set up correctly, try this next. Disconnect the SATA drive and check the BIOS. If necessary, disable the SATA ports and concentrate on the two IDE drives. Your boot drive should be the Master on the first IDE port (usually Port 0), and the data drive should be either the Slave on that same port or the Master on the other IDE port, depending how you connected them. Try getting the machine to run properly that way. Make sure the BIOS Boot Priority is set to use only the one drive that it should (maybe after your CD or floppy drive).
When you have that working, go back in to reconnect the SATA drive, making sure to reset the BIOS to enable its port(s), and checking again the Boot Priority to be sure it does not try to use this SATA drive or the data-only IDE drive. Should be able to boot and run with all three drives showing.
Watch for a small possible confusion. Often the best way for a mobo to handle a SATA drive is to set the BIOS to use it as an emulated IDE (or PATA) drive. That makes things easier for the OS to handle it. But when you do that, you may find the BIOS display starts calling the SATA unit an IDE drive or a SCSI drive. That may be slightly confusing, but the drive sizes usually will help you keep straight which is which.
Once you've done all this, you may have drives with "wrong names". Windows used to (maybe still does) assign letter names this way: C: is the Primary (Port 0) IDE Master, D: is the Secondary (Port 1) Master, E: is the Primary Slave, and F: is the Secondary Slave if it exists. Then it assigned the next letter to the next device, like SATA Port 0. If that's what your system does to you and you like it or can tolerate it, OK. But often that is a problem because your system already is set up with the CD drive as D: and it depends on finding CD items there, or something like that. If you need to change drive names after they are all working, you can do that through the Disk Manager. When doing that you can't (even temporarily) use the same letter for 2 devices. But you can create "space" by assigning unique letters, even if only temporarily, to each device, and then coming back to re-assign the final names to each.