What is wrong with my Mac?

[MORMOR8]

I have an OSX 10.4.11 which is about 4 or 5 years old. It is having freezing issues and there are times when it will simply go black and sometimes shut off. On the screen there is a line that goes about 4/5 of the way across and looks like it is missing pixels. I have run Tech tool which indicated a Video Ram failure. I followed all steps for correction including reinstall the OS and contacting AppleCare. AppleCare could only suggest that I take it somewhere for repairs. I believe it was the person to whom I spoke at AppleCare who said it is a Medium write error. A Mac repair person to whom I spoke on the phone said it is the logic board, and that I should consider buying a new computer. I hope someone has some insight on this.