I agree with the 2nd poster. I've seen quite a few of those from HP/compaq actually. I don't usually do the solder fix like him, but I think there was actually a lawsuit at one point with various companies over those graphics chips, as they would run very hot. There are solder joints connecting the graphics chip to the mainboard of the laptop. If my understanding is right, the graphics chips would overheat and cause the solder joints to break, giving you the condition your laptop is in.
The fixes would be that you can try to use a heatgun to heat up only that chip and it may basically cause the joints to go back together enough to make it work. Who knows how long that repair will last though. You can also have the motherboard replaced, which would solve it, but in a year or two, you might have the same things going on. If you know how to take things apart and fix them yourself, the cost is not bad. But to take them to a technician, you might honestly be better off with a new machine.
If you call around to some shops, check out their pricing. But another good option is this.
1. Remove the hard drive from your laptop.
2. Buy an enclosure, you can usually get them for about 5-7 dollars on ebay.
3. Sell your laptop as is online via ebay or amazon, I sold an older non working one for like 80 bucks once. But they may go for more as some guys buy them for the parts or to fix.
4. Take the money you would have used for repairs, and what you sell your old machine for, and buy a newer one. Then you also have your drive in an enclosure, which means that you've got all your old data as well.
I know you can get Acer computers fairly cheap, if you have a store near you called Microcenter, check them out. There is one near me that actually has Acer and Asusu laptops right now for 299.99. That is with Dual core Pentium processors, 4 gb of ram and I think a 320 gb hard drive. My wife has an acer, 2 years old, going on 3. Solid as a rock. That thing gets a lot of use. It almost never is off, usually sleeps, she's always on youtube, facebook, doing bookwork, etc. The only thing wrong with it is she needs a new battery, which is like 13 dollars on amazon.com.
I have an acer also, an older one with an nvidia chipset similar to yours and my temperatures for my graphics chip were VERY high. Running like 90 something degrees celcius at idle, which is nearly failure point. I actually modified the cooling inside my laptop(bent the heatpipe so that the heatsink for the graphics chip made better contact, and applied new thermal paste to both cpu and graphics chip). And the temperatures dropped on the graphics by about 30 degrees celcius.