The issue ended up being our java.exe had gotten renamed to java_bm.exe, java_ms.exe, and java_sm.exe so that it was easier to differentiate between the Method Server, Background Method Server, and Server Manager when looking at Task Manager. I thought the java.exe was left there but apparently it was not. Looking closer we are using a separate Java instance located at "D:\PTC\Windchill_12.0\Java".