Basically, your going about this all wrong. In you example, a failed lamp install could have just been fixed with sudo apt-get -f install Same thing with JDE. sudo apt-get remove name-of-package-here works for everything you installed via apt. If you installed via dpkg then sudo dpkg --remove package-name-here.

Missing or incorrect configuration can cause X (the GUI system) to not start. Usually you fix this is just a matter of removing /etc/X11/xorg.conf and then sudo restart lightdm. If that doesn't work you may need to re-configure your drivers. How you do that depends on your hardware and setup.

Removing repositories is dangerous. It's fine to do it. But when you install something via apt you install all it's dependencies. By removing a repository you could be removing more then the repository for just one package. apt will leave the old debs installed (from the disabled repo) but they will be "orphaned", meaning they will never get updates again (unless there in another repo). This is even more problematic if your using a "nightly" repo that supplies dependencies that are shared by many repos. apt will always use the "latest" version, but that version is in a repo that no longer exists.

Re-installing is silly. You should NEVER have to re-install Ubuntu, short of a hard drive failure, or partitioning mix up.

For backups: I recommend back-in-time. It's very easy to use. You should backup your $HOME directory and probably /etc/. Don't even bother backing up the rest. The only exception would be if you put files in an odd location.

One other side note. Won't load, is not that helpful. I am assuming, by your questions that X is not loading. The console is fully functional and can be used to fix problems with X not loading in very short order.

Stick with it. Once the learning curve is over, Linux is very easy to use and maintain.