OK, after kicking it around a bit, I am going to suggest a reinstall. But we are going to do it a bit different than you may have done previously.
First reformat your hardrive, in fact If you have just one partition on your harddrive, I am going to suggest doing and FDISK the drive and partition it into 2 sections. One is for all the software you install, and the other is for all of your data. If you do this, you can even make your e-mail client, and other software look to the data section for their files. I have been doing this since Windows 95, and it makes the reinstallation, or upgrade of the OS real easy, as well as backing up your data to a CD or DVD.
Either way, once you get the HD formatted, install the OS, then do a windows update right away. Once that is done, then create a restore point. Next install your firewall and Virus scanner, make sure they are updated, and create a restore point. Next install Windows Office, and update it, then create a restore point. Continue this until everything is installed.
After each time you do a restore point, then reboot the computer, and then look into the uninstall page (the one you did a screen pic of) and see if all the data is still there. If the data disappears, then you will know for sure what is causing the problem, and you will have a good restore point to go back to.
You mentioned a problem with installing Firefox, there appears to be a known issue with TalkBack (add-in)/Thinkvantage Password Manager (take a look at this.
Sorry I could not come up with an better way to fix your problem. This is the best way to find out what exactly is at fault and at the same time give you someway to go back without having to reinstall everything.