I think I've done something stupid and accidentally connected 12v to the 5v pin instead of the Vin pin. The ground was connected.
The board still shows the green light when I connect it to my laptop via USB but I can't upload a sketch to it.
The big chip gets warm to the touch but I don't know whether that's normal or not.
I'm assuming I've killed it, but would welcome any suggestions before I go & buy a replacement.
You likely damaged it if you can’t upload. The 5v pin is connected after the voltage regulator and is the line that powers the whole board including the main chip and serial chip.(assuming it’s a UNO)
Well let's do some debugging.
If you push the reset button, does the LED blink 3 times?
Also try the loopback test:
https://support.arduino.cc/hc/en-us/articles/360020366520-How-to-do-a-loopback-test
Thank you for the swift response.
No, the LED just stays on when I press Reset. Same if I hold Reset for 15 seconds.
WHen I connect the Arduino to the PC via USB & get 'device not recognised, device descriptor failed'.
I guess it's dead.
RIP 
Very dead.
That is a classic way of frying Arduinos. Always check connections before turning power on and never connect or disconnect wires with the power on.
Time for the recycle bin indeed...