A good place to start debugging a circuit is by looking at the SIM reader's pinout. SIM card readers have some voltages on their pins that should always be present in order to correctly detect and access a SIM card. The pinout (and some other useful info) can be found here: http://www.technoburst.net/2014/03/sim-cards-tutorial-part-1getting-started.html. You should measure the pins and see if their voltages are correct.
If all the voltages are present, you could start looking for the GSM modem on the board, see if that's getting power on its Vcc - pin, check if the trace to the antenna isn't interrupted, see if there's any kind of damaged filter in the way (some antenna's are used for multiple things, for example, the iPhone 4S uses one antenna for Wi-Fi and GPS signal and separates the two frequency bands with a filter. If that filter is broken, the signals are mixed and won't be received propperly by their respective chips).
Unfortunately, I don't know exactly where all the chips on the board are (and can't seem to find a schematic for this device). Sadly it seems that most of the chips are underneath some ESD - shields, so you'll need a heath gun to pull these off. But, if you have a heath gun and a multimeter laying around, I'd strongly encourage you to try and debug the board :)
Best of luck!