So, I had a faulty Acorn Electron. The problem was the ULA socket. In the earlier (I think) revisions the chip is socketed and the pins can break. Finding a replacement 68 pin CLCC socket wasn't that easy but I eventually found one.
You can see some more information on this problem here
I got the new socket...
De-soldered the old one (you can see the broken pins)
Soldered the new socket and put the chip in:
Closed it up, hoped for the best and switched it on:
If anyone else ever does this, just remember to make sure you put the socket in the right way (make note of which way the chip is facing).
----------------------------------------------------------------
I also made a couple of small modifications while I was at it. If you bridge LK4 you'll get colour output via composite (why this isn't enabled by default I don't know). Just stick a blob of solder on it.
And I turned the RF output into an audio socket. Just desolder the connection to the RF's RCA socket and solder a wire that goes from the +ve side of the speaker output to the RCA socket.
There's a hole in the side of the RF box that you can put the wire through:
