Adafruit 3G Module sends data but don't accept it
In situations like this I always recommend putting a scope on the signals in question. Looking at the voltages can reveal many problems that staring at the code will not, such as


Incorrect baud rates
Incorrect signalling levels (true RS232 vs. TTL vs 3V)
Incorrect pin assignments
Neglecting to set the TX pin as output
Excessive loading by pullup/pulldown resistors


If the RX LED is blinking then something is getting out. Try to determine the baud rate by looking for the narrowest pulse width. Check the RX line to see if any kind of response is coming back, if so check its baud rate and make sure both TX and RX use the same voltages.