I strongly advise to never update when a new OS comes out. They always take at least one year to fix all the bugs. Here is a check list from Apple Support:
Check for display issues
If your Mac doesn't appear to turn on, it's possible that the computer is turning on but the display isn't working. To see if it's a display issue, press your computer's power button. Then check for these signs that your Mac is turning on, even if the display remains dark:
You might hear a startup chime.
You might hear fan or drive noise.
If your Mac has an LED sleep indicator, it might turn on.
If your Mac notebook has a backlit keyboard, it might turn on.
When you press the Caps Lock key, the key's light turns on.
If any of these things happens and your Mac is connected to an external display, get help with video issues on external displays connected to your Mac. Otherwise, continue to the next section.
Check for power issues
If your Mac won't turn on and you've ruled out display issues, try these steps:
Make sure that the power cord and adapter are securely connected to your Mac and plugged in to a working electrical outlet. Plug in a lamp or other device to make sure the outlet works.
Try another power cord or adapter if the outlet works but your Mac still has no power.
If you're using a Mac notebook, make sure that you're using the right power adapter and cable and learn about troubleshooting MagSafe adapters. Leave the power adapter connected long enough to provide an adequate charge to the battery.
Check for other issues
Try these steps if you've ruled out power and display issues:
Disconnect all accessories that are plugged in to your Mac. This includes things like printers, USB hubs, and mobile devices.
Hold down the power button for ten seconds. Then press the power button again to see if the Mac turns on.
Reset the System Management Controller (SMC).
If you recently installed memory or a drive in your Mac, make sure that it's compatible and installed correctly. If possible, reinstall the original memory or drive to see if the issue persists.
If your Mac still won't start up after you've tried these steps, contact Apple Support. You can also visit an Apple Store or Apple Authorized Service Provider for help.