I installed a fresh patch of msi with validated code in my server. However, the CME does not load and just freezes as below. Where do I start looking for the error?
Open firebug or some sort of debug tool.
You'll find a call that looks more or less like this:
http://servername/WebUI/Editors/CME/Views/Dashboard/Dashboard_v22.214.171.124920.11_.aspx?mode=js (in your case that v6.1... should probably be v7.0...., since you are on 2013 GA).
Copy that URL and load it in the browser, it should show you a .NET error trace that will help you identify what failed. The most typical cause is that an extension is mapped to a file location that doesn't exist.
You can use chrome developer tools to see what's causing the error.
There are very good resources on SDL Live Content site for UI Troubleshooting, check below link.
Troubleshooting browser-based user interfaces (Login Required)
Adding the URL to the local intranet also fix this "White screen of death" in some cases