LinuxMCE selects the partition to boot off of based on a unique partition ID. If you changed hard drives, then this ID will be different.
To boot temporarily hit "e" during the grub boot, you'll want to highlight the kernel /boot/blahblahblah line. Hit "e" again. Change root=UUID=234234234234234234 to root=/dev/sda1 or /dev/hda1 depending on how your system is setup. Then hit B to boot the system. Once booted you'll want to run the blkid utility and modify /boot/grub/menu.lst and change the part after UUID= to match the UUID of the partition you got from blkid.