How did you install Fedora 21 on this machine? Which image did you use?
There are some things you might be able to do (e.g. switch to a different login manager and see if that helps) but let's sort out what you're even running before I recommend that
I typed the exec gnome-extension into the terminal and I am now on a new terminal line but the [David@localhost] thing has not appeared on the new line.
You got a comment on the question to the effect that it could be a video driver issue which is quite likely (usb errors notwithstanding). If this is the case trying a different desktop environment (e.g. xfce) might help. The fact that you don't have an internet connection makes this difficult though.
Alternatively you could try starting Gnome in classic mode, that might require less graphically
Not very helpful. Definitely sounds like a problem with gnome though. You could try installing another DE (I'm using KDE, xfce and lxde are more suited to older machines though) - is reinstalling a valid solution for you?
It may be possible to resolve the problem in other ways but that would likely be easier and is practical if you don't have any data on the machine yet