A couple days ago I came across this video on Youtube. I haven't seen any news posts on hacking this particular Kindle, so I'm posting this to see what turns up.
This is a very simple hack, and it actually isn't one. This video shows you how to enter the debug mode for the K4. You need to first create a text file on your K4. Give it the name "ENABLE_DIAGS" and make sure that it has no suffix. Then restart your K4 (from the settings menu).
But before you attempt this, let me strongly urge you not to - unless you already know how to create hacks. This isn't a hack which performs a specific task; it instead opens up your K4 so you can do things that Amazon wouldn't approve of. There are many things you can do screw up your K4. In fact, mine is frozen at the moment (whoops).