Faulty graphics chip, MacBook Pro 2011

Don't think your problem is the graphics chip or a logic board issue. If it was you would have a more definitive problem.

First I would do the basics here:

• Make sure you have a backup of your stuff before proceeding. Using the recovery CD the system came with or a bootable external HD or thumb drive run Apples' Disk Utility program to make sure the disk is in good health. If the disk was more than 3/4 full I would run a defrag app like Drive Genius (others will work as well here) to clean things up. I would also clear off some space as a 500MB drive might be on the tight side as the OS needs some space. You may need to look at getting a new HD here.
• Install a temperature monitoring app like Temperature Gauge which you can download from the app store (others will work as well here). See if the system is running hot. If it is then it may need a good cleaning and re-freshing the thermal paste on the CPU & GPU chips.
• Make sure you have a good anti-virus app running and have the latest definition files for it. Run a full sweep on the HD and if you find anything check your external HD & thumb drives.
• Make sure you have the latest OS & App updates running on the system. Then using Activity Monitor make sure nothing is hogging the CPU for cycles use google to ID any processes you can't ID. make sure you know what it is before you kill the process.
• Think about putting more RAM into he system 4GB is on the light side for Lion & Mountain Lion think about 8GB or if you can swing it go with 16GB. In any case make sure to check your Firmware EFI & SMC firmware updates for Intel-based Macs

I think you'll find during this process your problem will disappear.