I mounted the HDD in another PC I had sitting around and booted it using Ubuntu Live CD.
First, boot Ubuntu.
Second, install the needed tools:
$ sudo apt-get install lvm2
Third, load the modules to do our task:
$ sudo modprobe dm-mod
Fourth, scan the system for LVM volumes. Look for the volumes you want to mount. Typically this will be VolGroup00:
$ sudo vgscan
Fifth, we need to activate the volume(s):
$ sudo vgtchange -ay VolGroup00
Sixth, Look for the logical volume containing the root file system. Typically this will be LogVol00:
$ sudo lvs
Seventh, create the directory to mount the drive:
$ sudo mkdir /mnt/restore
Eighth, Mount the volume to the directory you just created.
$ sudo mount /dev/VolGroup00/LogVol00 /mnt/restore -o ro,user
Ninth, Copy your files off of the drive.
$ cp /mnt/restore/some/dir/and/path /some/dir/and/path
Tenth, Setup what ever backup means you have on the new server!
All in all this wasn't a terrible thing, it could have been much worse. I have since moved the nagios setup to a virtual machine and am backing it up nightly.