Your problem is most likely because you have Grub installed to the MBR (Master Boot Record) of a drive other than the drive where Grub's boot files are (i.e. the Ubuntu partition). When you connect your other drives, that changes the BIOS boot order, so Grub in the MBR looks on the wrong drive for its boot files and can't find them. I think the most ideal solution to your situation is if you can change your BIOS to boot the Ubuntu drive on start up; in other words, make the Ubuntu the first drive in the BIOS boot order. You'll need to install Grub to the MBR of the Ubuntu drive to make it bootable, and you can do that by first opening a terminal (Applications > Accessories > Terminal) and doing:
sudo grub
grub> find /boot/grub/stage1
grub> find /grub/stage1
One of the above commands should return your main Ubuntu partition (or /boot partition if you have one) in the form of (hdX,Y) where X and Y are numbers, for example (hd1,4), but use whatever it returns as follows:
grub> root (hdX,Y)
grub> setup (hdX)
grub> quit
Please post the output of all the above commands. Then if you reboot and set your BIOS to boot the Ubuntu drive, you should at least get the Grub menu. See if you can get that far or let me know if you run into problems; we can work from there if you want. :)