I've started getting electric shocks from the computer case.

I've tried two different power supplies - I get shocks with both.

They are too strong to be static electricity IMO.

I put a voltmeter between the case and a rad pipe. I can't measure any
voltage on AC or DC, I've tried all the voltmeter settings up to 500V.

I've tested the voltmeter on a mains wire - it reads 230-240V
reliably.

Interestingly, if I use the circuit tester function, there is a
circuit present between the rad pipe I was using as ground and the
case. Could they both be at the same potential maybe?

Nick