When you moved the partition you did so by file-copying. The boot loader, residing in the boot sector, is not part of the filing system so it cannot be copied although the necessary Grub files will be available in the new location.
It sounds you have Grub2 which uses /boot/gryb/grub.cfg as the configuration file instead of /boot/grub.menu.lst used by Grub1. Although both Grub use the same command "grub-install" there is a slight difference. I assume you are using Grub2 as it is more difficult to restore.
You need to boot up the PC with the same Live CD as the moved Linux as it guarantee the same commands available and the device detection, showed in /dev, matching your installation.
Basically you invoke the grub-install available in the Live CD, mount the partition , ask Grub2 to use it as the roor directory and then specify a destination, which can be /dev/sda3 if Grub2 is to be inside sda2 and /dev/sda if it is to take over the MBR. The former allows the distro "chainloadable and you can have both of them restored. A chainloadable distro can be booted by every PC boot loader, including Grub1 and Grub2.
Much what you want to know is inside the Live CD by just typing
The exact command you need in a root terminal should be
mount /dev/sda3 /mnt/sda3
grub-install --root-directory=/mnt/sda3 /dev/sda
The above commands are (1) create a mounting point in /mnt of the boot up Linux and call it /mnt/sda3 (2) Mount the device /dev/sda3 on /mnt/sda3 and (3) Ask Grub to install itself using the system files inside /mnt/sda3 and link them to the MBR of device sda.
There are a few good Grub2 guides knocking around a decent one can be found in Kubuntu forum. If you uses Grub1 check out the information in my "just booting tips" of my signature.
You you still have a problem you can fire up the distro manually. Let us know your progress. I have just moved 4 MS Windows and about 40 Linux from a 1TB disk to a 1.5TB disk myself.
You can move any number of distros by a simple script, say you need to move sdb5 to sdb30 to sda5 and sda30
for ((i=5;i<=30;i++)); do mkfs.ext3 /dev/sda$i; mkdir /mnt/sda$i; mount /dev/sda$i /mnt/sda$i; mkdir /mnt/sdb$i; mount /dev/sdb$i /mnt/sdb$i; cd /mnt/sdb$i; tar cf - . | ( cd /mnt/sda$i; tar xf -); done
You have to restore all the boot loaders but Grub1 is a lot easier as you can do them with a Grub prompt in one go.