distorted screen

recently as use my laptop the screen will become distorted and freeze up. i have to manually shut it off and restart by pressing the power button. can some please help me fix this.
i took a picture of the last time it happened with my cell phone
http://www.imagebam.com/image/c790647719913

Hello, Can you tell me what programs are you using when this happens? Are you performing the same task or is this random? It may be a conflict with a program that you are using, a video card going bad, a screen going bad, too much graphic acceleration, Etc… Do you have an external monitor that you can use for testing?

i am normally using different programs. internet explorer the last couple of times. but the most recent one did it when i was running a memory check. i have a 52' lcd i can hook up using vga cable. do you think changing the memory will fix it? i called hp and some guy told me $298 to replace the mother board. the only benefit of that was it included shipping! im thinking about getting a lenovo ideapad Y510-77582FU 98910. but i would like to fix my hp or else i will be out of a personal computer for 1-3 months.

called hp and some guy told me $298 to replace the mother board.

It is his job to sell you new items, not fix what you have.
Do you have the technical ability to remove the RAM, and then reseat it?
Oh lets start with removing the software that you are using to do a memory check.

my new problem is the laptop will no longer turn on. i woke up this morning and pressed the power button. the power light came on but nothing happened. i plugged in the power cord and the light that usually lights up when the cord is plugged up did not come on. i held down the power button three seconds to turn it off. i pressed the power button again to turn it back on and nothing happened. do this mean its the motherboard for sure? im typing from my moms computer now. ps when i did the memory check with the other program it found no errors and i let it run to 586%. i then used the memory tester that microsoft loaded into vista and that came back with no errors also.