davidleroux1, you said you wanted to keep all your data on the second partition?
1) Edit menu.lst in /boot/grub so it can boot to the second partition.
2) Backup all the data onto the second partition.
3) Install Mandriva onto the third partition.
4) When partitioning your drive with the Mandriva installer, set the second partition to
mount at "/backup" (or something like that).
5) Copy what files you need into your home directory.
6) Format the second partition.
7) Re-mount the second partition, and copy all the files you wanted to keep into the
newly created & mounted directory.
I've done things like this before - where I try to "poly-boot" my computer with more than one OS. Basically, it's asking for trouble, but you can make it work with some luck.
One thing I suggest is, next time you re-partition your hard drive, make room for a 10GB partition (or whatever you see fit), and mount that as your "/home" directory. Pretty much, always keep your data separate from your system (words of wisdom from my dad - a Bell UNIX system administrator).
EDIT: In my opinion, Lilo > GRUB.
I was brought up on an old Solaris SPARC5 system running Solaris 7.