My friend brought his brand new Uno R3 ( bought last saturday from one of the largest official stockists) for me to test. Loading any sketch produce the same results, connected to usb or external supply.
1) While connected to computer USB, load sketch, say "blink example" It appears to load ok with the leds flashing during data transmission, program runs ok with on-board LED flashing as it should.
2) Press the reset button, program stops and does not restart until program is re-loaded. Disconnecting usb and reconnecting has the same effect as pushing the re-set button. It is the same if the re-set pin is used. I checked the re-set switch and it is mechanically and electrically fine.
4) Do the same test but with a nine volt battery connected to the power input socket, load the sketch, remove the usb and the re-set button works once (program stops and re-starts) and then freezes again until the sketch is reloaded.
5) Doing exactly the same, on the same computer with two of my boards and the re-set works properly every time.
It would appear that the board is faulty, but a second/third..... opinion would be appreciated in case we are missing something.