What to do about "system running in low-graphics mode"?

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http://askubuntu.com – My Dell which was 5 years old suddenly karked it and I had the "low graphics" black screen and useless dialogue box. As I believed it was a dead graphics card I went out and bought a brand new machine. I put aside the new machine and tried again in vain to open the Dell. I eventually got to the command line via Ctrl+Alt+F1. I logged into my account from there, and simply started a series of sudo apt-get remove of various softwares that I knew were installed on my PC (software without any great consequence like Google earth, tweak, Skype etc). Lo and behold after a sudo reboot my computer (HowTos)