Start up problem, shuts down before it boots up completely

Do you see the Apple logo with a progress bar? If so, there may just be a problem with the operating system. Shutdown the computer, then power it on while holding Command + R on the keyboard (you can release the keys when you see a progress bar). This will boot the computer into Recovery Mode. From there you can go to Disk Utility and run First Aid on the internal storage drive. If that doesn't allow you to reboot, go back into Recovery Mode and reinstall the OS. If neither of those two options help, you may have a hardware issue, in which case you may need to open up the computer to figure out which component is failing.