have I got the correct mains adapter

peter Vidal, measure the output of your AC adapter with a multimeter on the barrel adapter. It should measure 19V-20V. If you have the right voltage, you can assume that your AC adapter is working. If that works, than you want to disassemble your computer and measure the voltage at the DC jack to make sure that you have the same voltage on it. If that works, you want to check your board for any missing or burned component, it is possible that your DC-DC circuitry on the logic board has issues. Also, check the power button to make sure that it is working. You can download the service manual for your computer on the bottom of this page. Hope this helps, good luck.