Well you made an assumption that is wrong, so maybe you can change this.
Any real IDE port can support up to two devices, so they need to be differentiated somehow. For that purpose every IDE device has a jumper pin set to choose between Master, Slave or sometimes Cable Select. Those terms are relevant ONLY to the particular port the HDD is connected to. There is NO such thing as a Master Drive for the entire computer. You assumed that, because you already have a SATA HDD as your BOOT device, it must be the Master in the computer, and hence the added IDE unit must be a Slave. Wrong.
Now, SATA does not do things that way - only one driver per port. The adapter board you got converts from a SATA connection to IDE and basically creates an IDE port for the old HDD to connect to. But like any other IDE port, it MUST have a MASTER device attached, and that is the ONLY device you can attach to that adapter board. So, set the jumpers on the old IDE drive to be the MASTER.
The matter of AHCI versus IDE Mode may be trickier. That was a work-around stuck into mobo BIOS's when SATA first arrived. At the time, the dominant OS was Win XP, and it did NOT come with a built-in driver for the new SATA devices that prefer to use new features in the AHCI protocol. There was a way to install new drivers for that, but the easier way many used was this little setting in BIOS Setup. If you choose IDE Emulation Mode for your SATA port, it limits that port to using ONLY the slightly limited set of IDE instructions and fools the OS into believing the HDD unit really is an IDE device, so it works. Some mobos had that setting available individually for each SATA port so you could set them differently, but most make that setting apply to all the SATA ports. That can cause what you saw. You have a SATA drive that has always been used as an AHCI device. If you then tell the port to treat it as an older IDE device, the OS is using the wrong driver and it won't work. So there are two possibilities yo can try with what you have. One is: look closely at where and how the IDE Emulation and AHCI Mode selections are made. IF you happen to have a mobo where they can be different on different SATA ports, set only the one for the old drive (with its adapter) to IDE Mode. Alternatively, set it to AHCI mode for all drives, and you will be able to boot. THEN look closely at the old IDE drive (assuming you have made the jumper change to Master) and see if you can READ it. If you can, I highly recommend you do NOT do any WRITE operations on it at all. Just copy everything you can from it.
If that still does not work, then you are back to getting a simple IDE HDD Dock that connects to your computer via USB. As RodroX has said above, that will not be affected by the IDE versus AHCI Mode thing. But I'm sure it also will want the drive's jumper to be set to Master.