Make sure the +- pins are clean so the batteries make contact. Also try plugging it in without batteries and see if it works.
You can also plug it into your pc or laptop, keep your finger on the power button and see if the computer picks it up.
I am not sure what else could be wrong with it, sometimes components can dethatch from the mainboard, might be worth opening it up to have a look. I am sure you can find a tutorial on here for 360 controller disassembly.
Good luck.