Black Screen - "Mainboard Problem". Please help me out!

hello.

please help me fix this laptop.

​after power on everything works but nothing shows up. some times after 10 or more power on finally it gives the display. but after a restart it dies again.

i have tried this:

-connected laptop to ​a monitor through VGA output, but nothing showed up.

-i removed ati graphic chip from the main board using hot air gun in order to force the laptop to use cpu graphic. and still nothing shows up.

-cmos battery gives 3v properly.

-i replaced cpu, ram and hard disk.

​and now out of hope i'm seeking international help and advise.​ - Please help me out!

i have a multimeter, can someone tell me where should i look???