This issue occurs on Amazon EC2 Micro instance, which comes with openjdk.

[ec2-user@ip-10-112-222-31 ~]$ yum list installed | grep jdk
java-1.6.0-openjdk.x86_64 1:1.6.0.0-1.20.b17.12.amzn1 installed
java-1.6.0-openjdk-devel.x86_64 1:1.6.0.0-1.20.b17.12.amzn1 @amzn

java.lang.NoClassDefFoundError: Could not initialize class hudson.security.SecurityRealm$CaptchaService
hudson.security.SecurityRealm.doCaptcha(SecurityRealm.java:311)
sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
java.lang.reflect.Method.invoke(Method.java:616)
org.kohsuke.stapler.Function$InstanceFunction.invoke(Function.java:259)
org.kohsuke.stapler.Function.bindAndInvoke(Function.java:126)
org.kohsuke.stapler.Function.bindAndInvokeAndServeResponse(Function.java:65)
org.kohsuke.stapler.MetaClass$1.doDispatch(MetaClass.java:79)
org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:30)
org.kohsuke.stapler.Stapler.invoke(Stapler.java:537)
org.kohsuke.stapler.MetaClass$5.doDispatch(MetaClass.java:181)
org.kohsuke.stapler.NameBasedDispatcher.dispatch(NameBasedDispatcher.java:30)
org.kohsuke.stapler.Stapler.invoke(Stapler.java:537)
org.kohsuke.stapler.Stapler.invoke(Stapler.java:453)
org.kohsuke.stapler.Stapler.service(Stapler.java:135)
javax.servlet.http.HttpServlet.service(HttpServlet.java:717)