You need to reinstall GRUB onto the working Ubuntu partition. Grab a Ubuntu LiveCD and boot to it.
One you do that, open GParted. We'll use this to discover your hard drive's letter and your Ubuntu partition's number.
Now, the underlined part at the top is the device we are looking at (my hard drive) where the underlined part inside the table is my Ubuntu partition (it won't be in the exact same place in the partition, look for an ext4 (or ext3 for Ubuntu versions prior to 10.04) partition). We need these two when we go into the terminal.
Next, open Terminal up and type the following in, replace X with the hard drive letter and Y with the partition number (these two are shown inside GParted)
sudo mount /dev/sdXY /mnt
sudo grub-install --root-directory=/mnt /dev/sdX
So for my example, I'd replace X with a and Y with 4. (these will vary depending on how your partitions are setup, so do not use these unless GParted says that's where your partitions are at)
Let it work and after it finishes, GRUB should show up when you boot your computer up.