Here are some things you can try without buying anything expensive.
It could be bad RAM.
Remove all of the RAM sticks, (including the ones under the keyboard if you have them there)
Try them one at a time in RAM slot 1, which is underneath your laptop labelled 'RAM 1' If none of them work, try them in 'RAM 2'.
If the computer boots, try the remaining RAM one at a time in the different slots.
It could be something weird with the CMOS battery,
Remove keyboard
Unplug the watch battery, it's in the middle with a pair of red and black wires (WARNING, the plug can be fragile)
Wait a minute, plug it back in.
Put keyboard back and try starting computer.
It could be faulty video card (make sure you have thermal paste for this)
Remove bottom panel
Remove heat sink on the right (screws are numbered)
Remove videocard
Try turning laptop on without videocard in it.