What does this mean:

hdd lost interrupt drive not ready for command

Actually, several things can cause that:

1) A flaky or loose cable connector.

2) An overheating HDD.

3) An overheating CPU/motherboard.

4) Bad RAM.

5) A failing SMPS.

Should I try to mount this drive? When I run "df -h", the drive doesn't show up. Here's what I get:

box:/$ df -h
Filesystem Size Used Avail Use% Mounted on
/dev/hda1 19G 3.2G 15G 18% /
tmpfs 31M 0 31M 0% /lib/init/rw
udev 10M 36K 10M 1% /dev
tmpfs 31M 0 31M 0% /dev/shm


I thinking that maybe I need to backup the data on the drive and afterwards follow this guide :
http://www.skullbox.net/newsda.php

I am on the correct track? Could this be why I get the "hdd lost interrupt drive not ready for command" errors?

backing up the data would be definitely a good idea as it seems your hd could by dying so save your data while you can

Yes, that's why you're getting the error, and yes, you NEED to back-up the data ASAP, if it's even still possible.