When you delete a partition, the hard disk partition table will change.
Your previous working partition might become unbootable.
To figure out what is the new partition that still has your old and working installation, what you can do is:
1. boot from Live DVD/CD,
2. open a terminal, type
look for the line that looks like your old working installation, such as
/dev/sda15:Linux Mint Xfce Edition (1):LinuxMint1:linux
the highlighted is the partition you want, yours would be different.
3. mount the new partition with
sudo mount /dev/sda15 /mnt
4. reinstall grub with
sudo grub-install --root-directory=/mnt /dev/sda
5, if no error on last line in terminal, then, reboot to check if grub is back and working.