Yes, you should get 5V out of the regulator with no load.
There are often small (less than 1uF) capacitors on the output of the 7805 regulators, sometimes tantalum. These have a nasty habit of shorting. Also they could be polarity-sensitive and will do strange things if put in backwards.
Cutting the foil at the output of the 7805 should tell you whether it's the regulator that's bad or a problem on the board. If you can connect a small load to the 7805 output (50 ohms would do) and still measure 5V, then the regulator is most likely good.
