During bootup fsck is scheduled to run and comes across some disk errors and needs to drop into the root shell. When run, a seg fault occurs and the system reboots, ad infinitum. Of course, it is possible to skip the check but this is not desired. Dropping to runlevel 1 to umount the partition w/ ubuntu on it to run an fsck is impossible as dropping into the root shell here fails too (the option is presented in a menu).

Is there a way to unmount the partition w/ ubuntu on there and fix the fs errors? I don't have a live cd or a way to burn an image. This machine does not boot from USB memory sticks.

thanks

Is there any way you can get a linux live CD of any kind?
You must have had an install CD in order to install Ubuntu. Do you still have it?
If you can boot from any type of linux live CD, just run (as root or with sudo):
Replace Xy with the drive and partition # of your Ubuntu root partition, Then reboot into your system without booting the live CD.