It boots fine if the hard disc it is on is the only one connected... boot from the boot menu when starting the computer(I do not want a dual boot), it gets stuck on the 'Busybox'... I do not want to disconnect the drives each time I want to start 'Mint'.
Well... That is the way you installed it. It appears that you installed Mint with only the one drive connected. When you plug the other drives in, the drive partition designators change from what it was on a single drive to the multi drive setup. You say that you don't want a dual boot, but at the same time you don't want to have to manually swap drives. You can't have it both ways. If all the drives stay connected and you wish to select which of the two OSs to boot, that is by definition a dual boot system.
And yes, if you install Ubuntu the same way, you will get the same result. I would suggest you rethink what you want to accomplish, read some of the partitioning and dual boot threads in the forum, and take a look at the user guide and wiki. If you do this you will have a much better chance of having a stable, serviceable system regardless of which distro you choose to install.