First, your organization should keep your software maintenance current with Oracle; while this might not provide you with patches for the current version, it would provide you the ability to migrate to a later, and better supported version. Unless you have IT support within your organizeation to fully support the application, you will be continually faced with living on the edge--such as you appear to be now.
Having said that, almost certainly your problems are incomplatibility with either the Java versions or the browser/OS you are running. I do not believe that any browser later than IE8 was supported in CM13.0, and for Java I believe that 1.6.0_14 was the certified version. If you are running JRE 7_51 this easily could be your problem. Also, if you are running any more recent browser (IE9, IE10) or any recent version of Firefox, these could also be causing issues.
This may not be the response you would like to hear.