Definitely sounds like a GPU/driver issue, unless you are noticing the extraction fans running very loud/fast and the wrist-pad/keyboard getting too warm.
Do you have the most up-to-date drivers installed for the 5870? Did the problem occur with prior driver(s) or not? If yes to the first question and no to the second, try rolling back the driver to a previous working version OR revert to the recommended driver from ASUS's website for your laptop model.
There are several threads (by checking Google) that show older G-series ASUS laptops, in particular the G73 model not playing nicely with certain ATI/AMD drivers/CCC installed beyond what's on ASUS's website. This may require an updated BIOS download/install, in order to run newer AMD drivers for the 5870, if they exist...
Lastly (or firstly), try connecting your laptop to an external monitor and see if the issue repeats... There are also several threads on this being a potential issue; laptop screen/panel failing.