So I bought the replacement motherboard from eBay, and all seemed well with
the machine running for around 10 minutes.
I closed the machine and left it to recharge its battery. When I came to
switch on, it wouldn't fire up, and I could hear funny noises which I
suspect was the hard drive beign powered on/off at something like 2hz.

After a bit of playing, it seems that this board is now dead also, except
that on this one the power and activity (hdd) lights are flickering very
quickly, and about one-third brightness.

Could there be a logical explanation for what might be damaged? Perhaps some
kind of capacitor which is needed to hold a charge and allow it to power-up?
What can I test with just a multimeter?

I have since noticed that the PSU is over-rated, at 4.5amps instead of the
machines stated 3.5A, but I thought that the additional current was simply
not used. Could this have been the cause of the problem?

I have now tried a more closely matched thinkpad PSU (3.36A), and it does
the same.

thanks for any help.