How to Repair 15" Mac Book Pro Core 2 Duo 2.16 Ghz That Won't Power On?
Solution 1:
In the absence of “chime” there are three things to blame: RAM, GPU or Board/CPU.
I know because I had the same problem throughout the years with different Macs (and even Powerbooks). Try removing some RAM and putting some other modules, also remove the battery as suggested by Philip in the comments.
Using an external display may help identify screen problems too.
And finally an Apple Store, even if it’s out of warranty, will diagnose the box (sometimes for free, it depends) sometimes for a small fee. Bear in mind they will always go for the brute force route: “you have to replace X,Y,Z”, 1000 u$s. Thanks for Coming, Bye. ;)
Solution 2:
In order of desperation:
Press Cmd+Alt+power for 3 seconds to start it. If you get a chime you're back in business.
Reset the pram: Turn on the computer and immediately press Cmd+Alt+P+R. Keep it pressed until you hear two chimes.
Reset the System Management Controller: Unplug power, remove battery, press start button for 5 seconds. Put the power back on, press the power button. You should have a chime or a series of loud beeps.
If nothing works, you have a motherboard issue. Loud beeps indicate a number of issues depending on the number of beeps. A chime and nothing displayed is most likely a display issue.
Reminder: The Altkey, also called option key, is the one with the mark ⎇ and the label Alt. The command key has the mark ⌘ and is labeled cmd.