My xbox got one ring with error code E79 or E71

Well, E79 and E71 are different things.

The E79 is an error code representing a Hard Drive error. It could be the HDD itself or its a connection problem with the hard drive. Try playing your 360 without it and see what happens.

E71: possibly a dashboard update error, there is no solution at present the console must be sent back to MS for repair. Try resetting your console, or Power Off, remove the HDD if you have it. Reconnect the HDD.