Multiple Memory Integrity Check Failures

I noticed a similar thread below mine, but the problem I'm having is that both memory cards in my Laptop seem to be corrupt. Being that this laptop is brand new, does failure of two memory cards at the same time seem very likely? They seem to have failed in more than one location on each card, as each test that is run it finds different addresses with errors. Is there any way to erase the memory and see if that removes the errors? I can't see myself going out to replace two brand new memory cards as was suggested in the previous thread.

In addition, yesterday before the cards failed, I was playing a video game and I noticed these distortions on the screen that kept happening in different areas, but I dismissed them at the time.

After installing AVG, the computer failed to boot on the next reboot and I ran a memory check, only to find a horribly corrupted set of cards a mere month after I bought it.

So far, the scans have failed every single time except for 2 out of about 100 scans of different memory blocks.

EDIT: After the memory tests finished, it rebooted to a flashing white line in the upper left corner and refuses to go any further. Rebooting doesn't seem to make a difference.