I cloned my Windows 10 installation from an HDD to a smaller SSD using Clonezilla. It was harder than I expected, but I was successful. Once my SSD installation was running smoothly, I used an Ubuntu Live USB to wipe my old HDD clean so I could use it as a secondary drive. Now whenever I try to start with the HDD connected, Windows won't start and will show the "Inaccessible Boot Device" message. I tried everything I could think of, and spent one hour on the phone with MS customer support. Their solution was to perform a fresh installation, but I'd rather fix this without losing all my programs and data.
Note: I lost somehow the hidden partition at the end of the drive, but it doesn't seem to affect my computer in any way.