This is way out on the bleeding edge, but it is possible that you have a device that is not properly shielded or grounded. The side of the case is causing a resistance in the magnetic field of that device and is creating a resistance which is causing it to draw more power to compensate. That is the only possible thing I can think of as to why it works fine with the side off, but when you put the side back on, it starts having problems. That's why I asked you to look at the edges of the case, I have seen where a single screw grounds a system and causes it to fail. And I have seen missing case grounds also cause problems. Granted both of these were in aircraft electronic systems, they were still computers.
If you put the side back on, and it causes problems, then you need to look at the grounds in the entire system, especially between the ground pin on the power connector, and the case and side of the case when it is installed. Look for missing grounds, and high resistance grounds.
Is that all as clear as mud?