... and you already tried reset SMC (unplug, hit power button, reconnect) and ruled out any devices connected.
I'd take it in while you can. You can also run AHT but I wouldn't expect it to find anything. And take a fresshly formatted drive and do a clean install.
What upgrades if any have been done? RAM included.Troubleshooting: My computer won't turn on
If your Macintosh computer won't turn on, here's how to troubleshoot it. Please keep in mind that although your computer may display similar symptoms that prevent it from showing video, this article discusses what to do if the computer won't turn on, meaning that when you press the power button:
- You don't hear a startup chime.
- You don't hear any fan or drive noise.
- The power button or power indicator doesn't light up at all.
- You may hear a startup chime.
- You may hear fan or drive noise.
- You may see the power button or power indicator light up.
If your computer won't turn on, try each of these steps:
- Make sure that the power cord is plugged into a working wall outlet, and that it's properly connected to the power adapter. (To check if the wall socket is working, plug in a lamp or other electrical device.)
- Make sure that the power adapter is properly connected to the power port on the side or back of the computer.
- Disconnect all accessories that are plugged into the computer, such as a printer, hub, or other mobile device.
- Reset the computer's PMU, SMC, or PRAM. Refer to the instructions for your model:
reset SMC For "Mac wont' turn on or boot" and related
General purpose Mac troubleshooting guide: Isolating issues in Mac OS X
Creating a temporary user to isolate user-specific problems: Isolating an issue by using another user account
Identifying resource hogs and other tips: Using Activity Monitor to read System Memory and determine how much RAM is being used
Starting the computer in "safe mode": Mac OS X: What is Safe Boot, Safe Mode?
To identify potential hardware problems: Apple Hardware Test
General Mac maintenance: Tips to keep your Mac in top form
And you unplugged everything other than mouse/kb... As for RAM, no one really buys from Apple, when you can get better with longer warranty for 1/3 the price.
sometimes you need spare good parts to troubleshoot. Could be video card, could even be memory - leave the side door off so you can watch.
So it is just shy of 2 yrs, still under Applecare you bought? and while I wouldn't hold out hope, if you can, that way yhou also establish date of problem beginning and make use of AC.
Apple Servcie or Store within hours drive?
And you are hopefully using a well respected UPS (minimum 1000VA, more likely 1500VA).
Me: I would outfit it wtih SSD and two more hard drives if you have not, and 24GB RAM - when you get it working properly.
In the meantime, duplicate you backup strategy and keep a good OS backed up, cloned and handy too.
I took it into the apple store, and even though I don't have apple care they reinstalled the operating system free of charge and that temporarily fixed the problem. However it is back again. Now I just live with it. I press the power button once...wait 5 seconds until I hear the click, and then press it again and it works.