Xbox 360 Controller Constantly Vibrates

When receiving any kind of power - through wire or battery pack - this Xbox 360 controller "pulses" momentarily with a small vibration. Turning it on results in it constantly vibrating at a steady rate from the right side rumbler, changing in accordance to input from games (i.e. shooting a gun in a GTA game).

I resoldered the battery contacts, resoldered the right side rumbler socket, and tried checking for other shorts while comparing to a (seemingly) identical board - with no success. Are there any ways to remedy this?