Welcome to the forum, FiveAlive.
I have gotten Mint to install and run on machines with a slightly slower processor than yours. I found out that the trick when having only 256 MB of RAM was to create partitions and add a /swap file in advance.
You can use a gParted CD, but I have been using a Linux Mint 5 Xfce Live CD. Xfce booted up better than the GNOME one. I used the partition editor to make my partitions, shut down the computer, rebooted with the GNOME CD, and the installation proceeded without any problems.
Yes, I could have used the Xfce desktop, but I like the GNOME one better. Those machines with 256 MB of RAM are used for Thunderbird, Firefox, and Rhythmbox. For those purposes, everything works fine. Perhaps it will work for you, as well. Good luck.