From what I can understand, this issue has nothing to do with Minecraft but with Java itself and its interaction with operating system libraries.
I recently got a new hard drive and installed the latest version of Java and the Java Development Kit (1.8.0_05) (I am a programmer so I have use for it). Since then I have been having this problem. Before I got my new hard drive, I had updated to Java 1.8.0 and copied it to a flash drive so I could play Minecraft on a computer without Java installed. The previous version of Java I had been using (JDK 1.7.0_40) was working flawlessly and I was able to interact with it very flexibly.
The problem arose when I updated to Java 1.8, I was using a program called Transparent Windows which is supposed to make a window semi-transparent to be able to view 2 windows stacked on top of each other (ex. Minecraft and a web browser). When I was using JDK 1.7 Transparent Windows worked as it should and allowed you to right click on the title bar and select a "Transparency" option.
This indicates to me that starting in Java/JDK version 1.7.0_60 (that is the closest I can find to 1.7.0_40 on oracle's website) Java has not been able to access or find Windows' native libraries, and as such becomes unresponsive in such a bizarre manner.
Track down a copy of the JDK 1.7.0_40 or earlier and launch the game using it, or try downloading the 32 bit (x86) copy of the latest Java. I have not extensively tested the 32 bit version but after a few hours of continuous play I have not had this "Not Responding" issue.
Note: Do NOT change the javaw.exe compatibility. I have tried this for multiple versions of java, and attempted changing compatibility for both Minecraft.exe (the launcher) and javaw.exe (Java). This appeared to work at first but after a few hours the problem came up again only in a different form. Instead of getting the "Not Responding" problem the game will instantly crash, giving you NO possibility of saving your game or disconnecting from a server safely. There is no warning when this happens, it will stop responding and instantly say that java has stopped working. At this point the only option is to "Close the Program".
Edit: I have now tested the 32 bit versions and have the same problem. Just find an old version of the java dev kit or JDK (between 1.7.0 and 1.7.0_40)