How do I figure out what is wrong with my xbox 360?

Overheating is the main cause of the freezing problem on your console. The defective cooling system makes the console overheated and your console freezes up. It does NOT necessarily display the RROD. This site might help with the trouble shooting Xbox 360 Troubleshooting

1.Do the xclamp fix. Xbox 360 Red Ring of Death Fix Kit It does work wonders and it only costs you a little and its not difficulty to do.

2. Do the 12v fan mod. Increased airflow of the 360 is not a bad idea see here how it's done http://www.llamma.com/xbox360/mods/360-1... (It will make the 360 louder)

3. Look into doing a reflow the motherboard.I recommend a professional reflow because you are using a lot of heat.

4. Open the case if u have no warranty left.:) Also make sure that it is not your power supply make sure that the power brick is not obstructed by anything. Those are of course just my suggestions and if you do a Google search you will see that there are many gamers out there with the same issues and multiple different approaches in how to fix them. Good luck with your console and let us know how it is going.