When installing Apigee Private Cloud patch 4.15.0.04.03 the UI component will not start unless Java 7 is being used.
This is an oversight, and should get fixed shortly.
In the meantime, if you need to use the patch, and are not using java 7 already please upgrade following the instructions to upgrade posted here:
https://community.apigee.com/articles/1704/how-to-upgrade-my-apigee-edge-opdk-from-java-6-to.html