Krodal:
Your programmer seems okay (you knew that already).
But you don't have any communication with the 'bad' chip (you knew that also).You don't know what the fuses are, since there is no communication.
You probably have a 'bricked' chip.Unbricking is done by either supplying a clock signal to the clock input, or with high-voltage programming.
Well, these chips are brand new - arrived in the post this morning from Farnell. I am tempted to send them back for a replacement, but I don't want to do that if the next ones are the same.
I don't have a high voltage programmer, but a clock is possible - tell me more. I have a 16MHz crystal on the board already (my ISP shield also has an ADM232 chip and DB9 for sketch uploading), which I know works as I have uploaded the good ol' blinky sketch to a known good chip on this board, but if I need to generate an external clock then I can do that. What frequency? What pin? Does it need to be synchronous with the programming communication?