Laptop will not boot

I was given an Asus X53S laptop to look at. After doing some testing I saw the hard drive needed replacing. I gave the person the laptop back and said what needs doing. About a week later they gave me the money to buy a hard drive and gave me the laptop back. Before I replaced the old hard drive with the new one I did not check if the laptop was still booting up. As it was booting up the last time I had it I just assumed that side of things was ok. I replaced the hard drive and then went to boot up the laptop. It won't boot. It's dead as a dodo.

Now I know if I go back to the person whose laptop it is and say it now won't switch on I will get the dreaded "Well it was switching on when I gave it to you...................."

I am going to borrow a multimeter tomorrow to check the external power supply is ok. Is there anything on the motherboard I could check with the multimeter in regards to the laptop not powering on?

Can anybody please suggest ideas of things to check. So far I tried taking the battery out and holding the power button for 30 seconds and the putting battery back and trying again. I have also tried leaving the battery out for 15 minutes and then putting it back in.