Graham,
This does not sound like a normal software bug. I would go for some addon software or a virus / rootkit that is doing this. My 1st impression is hardware, but since you have changed all this, I will go with malware.
How was the new system built -was it fresh from scratch or a disk clone? The later might preserve any nasty software .. otherwise it would point to it being elsewhere on the network.
This is very unlikely to be:
I hope that helps
David
(c)David Overton 2006-23