Check that the correct voltage is reaching the laptop from the PSU when you try to power it up, and there isn't a sudden substantial voltage drop.
Try disconnecting from the motherboard (often under the keyboard) the multiway connector feeding video and power to the screen (and invertor and lamp). Then plug in an external monitor.
I'd doubt if it's one of the peripherals, but try disconnecting hard drive, CD, WiFi board, keyboard and touchpad, and see if that makes any difference.
See if you can check the RAM on another machine. If applicable, reduce to one piece of RAM only.
You're now at the point where it looks like a motherboard fault. If you really feel the urge to progress further, you could try disconnecting the BIOS battery from the motherboard. This might involve substantial dismantling followed by unsoldering of the battery if there is no CLR CMOS jumper. But we're clutching at straws now...
ROGER - G0AOZ.