Why does it fail to boot properly

There are many reasons this can happen.

The first thing is to review your MagSafe power adapter to make sure its healthy and the battery is charging. Review this Apple T/N: Apple Portables: Troubleshooting MagSafe adapters Often the simples issue is the cause. Make sure the MagSafe is the correct one, the cable its self is not damaged, and the connections are clean and in good health. What is the color of the MagSafe plug Amber or Green? If you don’t see it lit at all you’ll need to try a second charger.

The next thing is to check the battery using the battery checker is it charged (8 lights lit)? If not your battery may need replacing.

You will likely need to disconnect the battery internally and try powering your system with the power adapter. Is the system able to boot up then?

Looking deeper will require access to an external drive with a known good working OS on not to see if the issue is the drive.