System model name: MacBookPro6,2
That particular model Mac was plagued with GPU problems, and I'm sorry to tell you that one is suffering from it.
Apple offered the equivalent of an "extended warranty" for that specific problem, but it expired a long, long time ago. Apple will no longer repair it, at any cost.
All hope is not lost. If you are bound and determined to keep that MPB alive regardless of the cost it may entail (which happens to be significant) non-authorized repair services are available. Contact this company: Mac Repair - Mac Parts and Service for Apple Macbook, iPhone ... Their repair method uses GPUs scavenged from discarded Macs, but uses materials and methods no electronics manufacturer uses any more (think RoHS). They are likely to tell you those GPUs are becoming scarce.
That's the bad news. Contact them and see what good news they may have to offer. PowerBook Medic has been around for a long time, they know what they're doing, they're reputable, and there's no way I would do what they do for what little they charge.