Does it do this with another different computer such as a laptop with VGA output etc. If it does the same thing on a different computer then its the display and may be why the old owner got rid of it.
Do you still have contact with the seller to return it if its broken or was this a blind sale with no ability to get money back such as at a flea market or sold as-is on ebay etc?
There was a flat screen 8 years ago that did the same thing and I diagnosed it down to a bunch of bad capacitors for the logic board for the display which was part of the display interface buttons. I was able to replace these leaking caps and the problem went away. I thought that the bad capacitor issue hit mainly motherboards and power supplies, but this dell display had electrolytics in it that were bad ones and the ripple was causing for the display control interface to think that the menu button was being pressed over and over again so the same symptoms of what you have with a flashing menu box for the display properties.
More info here:
http://en.wikipedia.org/wiki/Capacitor_plague
