Your system's first boot on its own power is what electrical engineers call the “smoke test”.
If the system fails to start up correctly, don't panic. If the installation was successful, chances are good that there is only a relatively minor problem that is preventing the system from booting Ubuntu. In most cases such problems can be fixed without having to repeat the installation. One available option to fix boot problems is to use the installer's built-in rescue mode (see Section 8.7, “Recovering a Broken System”).