I just started FUSE MB 126.96.36.199 with JDK 1.6.0_13 on my XP laptop and it starts fine, and loads the camel context without any problems:
INFO DefaultCamelContext - Apache Camel 188.8.131.52-fuse (CamelContext:camel) is starting
INFO TransportConnector - Connector vm://localhost Started
INFO DefaultCamelContext - Apache Camel 184.108.40.206-fuse (CamelContext:camel) started
Have you modified the config in any way or is this just a normal installation starting up? I suspect that perhaps you have deployed a camel route that is doing some JAXB marshalling? If that is the case you may be picking up the JAXB 2.0 API that ships with Java 1.6. If you place the jaxb-api-2.1.jar into $JRE_HOME/lib/endorsed, you will get the JRE to pick up JAXB 2.1 instead of 2.0.
Hope that helps.