IF there is no Hardware problem:
Installing a new version of Mac OS X starts with a Restart. This boots up a stripped-down version of the new, incoming software. The Installer in that new software then unpacks and copies files, getting ready for the complete version of the new software. When all appears to be going well, it begins moving files into position to run the complete new version at the next Startup. If that goes well it moves temporary files to the Trash and Restarts. This entire process typically takes 10 to 30 minutes (not counting the download time).
If it dies early in the process, especially before copying files into position, the Install process is intended to leave your original System in place, unmodified. So you should see whether you can still boot the old System before you take desperate measures.
If it dies immediately after the first Restart, your Mac may not be compatible with the new System, the download could be damaged, or there may be a Hardware problem.