Have the above laptop, and it simply won't power on.
Have done what Sony helpfully suggested and held down the power button for 15secs with and without the battery.
Have tested the AC power and its reading a 19.5v.
Hard drive is working ok with a 2.5" USB caddy - so all docs have been backed up.

Any ideas of the next step?

Thanks

Try powering on with various memory configurations, remove all, only one in each of the slots, and trying the diffferent memory in each of them This will eliminate the idea of a bad memory SODIMM or a bad slot.

can you tell us what was the last activity that you did before all this started