It sounds like the GSM module isn't turning on. You probably didn't fry it (or, at least, that's not the hypothesis I'd start with). Try checking the solder joints on the GSM module and the microcontroller. I annotated the relevant pins on the image here: http://www.flickr.com/photos/mellis/9162546146/
In particular, pwrkey lets the microcontroller turn the GSM module on and off. TX1 and RX1 are used for communication between the microcontroller and the GSM module. And, of course, the GSM module needs power and ground.
Make sure the pins of the component are actually soldered to the board but also that they're not shorted to the pins next to them (except for when there are multiple of the same pin next to each other, as with ground and power).