Carelessly I applied 12V to the 5V pin while breadboarding a project. 
I now get no signs of life from the board. And applying 9V via the board's jack socket from my bench power supply indicates a direct short.
I've placed an order for a replacement board but, expense apart, it seems such a waste. Is there a fuse anywhere or anything else I can try to repair it please?
(I've posted simultaneously here and to the AboutCircuits forum.)
Terry, East Grinstead, UK
It is pretty likely that you've killed the main microcontroller which can be replaced, but it is also pretty likely that you've killed the USB-Serial chip too. That's pretty hard to replace. You might just be better off getting a new Arduino, unless you think you're able to desolder the USB-Serial chip and replace it.
Thanks, appreciate the fast reply.
From extensive googling meanwhile I see there are many potential causes. But are there any definitive tests I can make to isolate the problem(s)?
In case it offers a further clue, with the 328 chip removed both the 5V and 3.3V pins are grounded.
I see nothing visibly wrong on either top or bottom of the board.
Do you think it would be worth replacing the 3-pin regulator chip next to the jack socket, an AMS1117?
I expect delivery of a replacement UNO R3 tomorrow.
Terrypin:
In case it offers a further clue, with the 328 chip removed both the 5V and 3.3V pins are grounded.
Are you testing this by applying power and measuring the voltage on those pins, or by testing for continuity when the board isn't powered?
Since there is still a power fault when the 328 is removed it is likely that there's a problem with either the USB-Serial chip or the voltage regulator. It is easier to remove the regulator. If I were you I would remove the regulator and then check for a fault condition- if it is still there then the culprit is likely to be the USB-Serial chip. Or also possibly the 3.3V regulator, depending on what board you have. Can you post a link to the board?
No power, just using my multimeter.
What puzzles me is that despite my bench PS earlier indicating over 3A when I connected 12v to the jack socket, the resistance across its terminals is 'infinite'.
The amazon.uk link had a staggering 861 characters so here's a shorter one!