You can check if the System or Application Event Logs indicate any Errors or Warnings prior to previous lockups as xeromist recommends. In the System Event Log, there will be an Eventlog EventID 6008 that states "The previous system shutdown was unexpected". This indicates the system lockup. You can filter for this event to see when your system lockups occurred, then clear the filter to see if any Errors or Warnings occurred previous to the lockup. You can use the time of the Eventlog EventID 6008 to examine the Application Eventlog to see if any Warnings or Errors occurred in it prior to the time of the System Event Log EventID 6008.

Check a couple of hours prior to the Eventlog EventID 6008 time and report the Event Source, EventID's, and text of the Errors and Warnings.

High GPU and CPU temperatures from gaming can result in the crashes you experience. The system shuts down to prevent heat damage. Install RealTemp or SpeedFan and monitor GPU and CPU temps. If they reach into the 90's C or higher, you'll want to attempt some cooling maintenance such as blowing out your fans and exhaust with compressed gas. There are videos on YouTube that detail this procedure. Repasting the GPU (http://www.asusrog.com/forums/showthread.php?946-G73JH-GPU-Overheating-Observations-and-Suggestions-...) may also be on your "to do" list.

What kind of G73 have you bought? If it's G73JH I read in this other forum that it could be a GSOD problem, and then the solution is to install the ATI drivers 10.1

As dstrakele said, try to keep track of your temps to see if the shutdowns coincide with a temperature spike. Another utility that I sometimes uses is speccy, but only use one utility at a time.

Did you put your battery back in and recreate the problem?

How old is your notebook?