That your mac is not backed up should be your highest priority -- I would go buy a disk and use Carbon Copy Cloner or SuperDuper to make a clone of your disk. In fact, if you are going to replace the disk, that is the simplest/fastest/safest way to do it -- buy a new disk in an enclosure, clone the old disk on to it, then swap the disks.
Once you have your data backed up, you can work on getting your machine to function better, and your Time Machine to work. Until then, though, you are definitely flying without a net!
If it turns out to be some other problem, and the old disk is and was always fine, you don't have to feel like you wasted the money. You would going forward have a handy spare disk in an enclosure that you can use to clone your system every month or so, independent of your Time Machine backups.
Thanks for the advice Cathy...however, I have a full Mozy Backup.
and, as I am looking at Time Machine it has everything up-to-date from early today. The problem seems to be that it is full and has not recycled. IEarlier today I could go back to July 6, now it is earlioer today.
Any ideas of how I can clear out Time Machine and start again?