My guess is you have a Early 2008 3,1 only because lately it seems so many do.
Had you tried Apple Hardware Test, hopefully (TTP 6 rarely does), and reset smc.
Do you have 3rd party controllers and devices that don't support sleep?
Also, try normal troubleshooting - I'd start with a fresh install and update and test with this system (clone as you go if needed) and only gradually add back in.Troubleshooting: My computer won't turn on
SymptomsIf 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.
ResolutionIf your computer won't turn on, try each of these steps:
reset SMC For "Mac wont' turn on or boot" and relatedhttps://support.apple.com/kb/TS1367
- 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:
General purpose Mac troubleshooting guide: Isolating issues in Mac OS XCreating a temporary user to isolate user-specific problems: Isolating an issue by using another user accountIdentifying resource hogs and other tips: Using Activity Monitor to read System Memory and determine how much RAM is being usedStarting the computer in "safe mode": Mac OS X: What is Safe Boot, Safe Mode?To identify potential hardware problems: Apple Hardware TestGeneral Mac maintenance: Tips to keep your Mac in top formApple Hardware Test
If you test a Mac Pro (Mid 2010 and later) with Apple Hardware Test (AHT), you might encounter an alert indicating that the computer does not pass the reading of the following sensor:
Note: "0.972" is a value and may vary.Although the diagnostic displays the alert that the hardware does not pass for this specific sensor, the computer can be considered as passing. The diagnostic tool does not intepret the sensor value correcly.