Most of the time motherboards / system will work with the modules they were designed for and there is some flexibility regarding speed, memory timings, etc., but in some instances boards can be very picky about the types of RAM that will work in them. Below is a list of the Fully Qualified Modules supported by your motherboard:
http://www.gigabyte.com.tw/FileList/MemorySupport/motherboard_memory_ga-g31m-s2l.pdfThere is only one DDR2 800 MHz 2 GB stick listed as qualified on this list, outside of these modules Gigabyte makes no guarantee other modules will work. The board may also be defaulting in the wrong voltage or timing settings. The specs on that Micron 2 GB module from the compatibility list are a voltage of 1.8 and CL of 6:
http://www.micron.com/products/partdetail?part=MT16HTF25664AY-800If you are using 2 GB modules from a different manufacturer make sure they support that same voltage and timing as the micron model and then make sure your motherboard is set for that same memory voltage and timing, you should be able to change these settings in the CMOS settings.
Good luck!