Ok so, while fixing your logic board they broke more parts? What the history on the machine (repair wise) and what is the warranty status. If not under warranty, did you pay to have the services provided?
This is very long but maybe it will help.
About a year or so ago the problem started, when I tried to start I would get a black screen and then the fans would go into turbo mode. I took it to The Apple Store and they quickly diagnosed it as the logic board. Because the computer was what I perceived to be not very old and gently used I was pissed so I took the computer with me. I did all kinds of research and found what you mentioned, these machines had a known problem of logic boards failing. People on various message boards suggested continually calling Apple, complaining and asking to speak with a supervisor. All of which I did, to no avail.
Then I heard a close friend had cancer and I decided to cut my losses and resolve myself that I had tried as hard as I could but getting Apple to repair it for free was a moot point. Half an hour after letting it go I received an e-mail survey from Apple regarding my most recent call to them. They wanted to know if I was satisfied with my experience. Needless to say I wrote a very long reply basically stating I felt the computer needing a nearly $600 repair when only being 3-4 years old was outrageous and that I bought Apple because I thought I was getting a quality product and was dealing with a company that cared as compared to just buying some random PC. I wrote that they had small time thinking when it came to their customers and instead of viewing me as a $2,500 customer (whatever the G5 and Cinema monitor cost me) they should see me as a $500,000 client because I had to decide whether my family was going to be an Apple family or a PC family and that I was directly responsible for at least another $5,000 in potential sales in next 6 months alone. In my immediate family (My sister was thinking of buying a Macbook, as was my Mother-in-law, my daughter and my wife was thinking of an iPhone etc....) alone. I explained that I was the type of person who when I was hot on something, went out of my way to let people know about it, that I was the type of person my friends, family and colleagues looked to when researching things and my opinion was highly valued in not only my immediate circle but also with friends of friends etc...
The next day I received a telephone call from someone at Apple who said they noticed I called and spoken with a number of their supervisors and was still unsatisfied so she offered to have the logic board replaced for free using and 'exemption code'. She asked where I wanted to have it fixed and she called ahead and set-up the appointment. I dropped the computer off that very night at 9:00PM and by 7:00AM the following morning, before the store was even open, a tech called saying my computer was fixed. He said all he needed to do was re-seat the video card. I picked the computer up and it worked fine. For a while. Whenever I would get the 'turbo fans' I would open it up and re-seat everything (I had no idea which one was the video card so I did them all). That seemed to work for a while. Until it wouldn't and I took it in again to The Apple Store. They kept the computer a few days and finally determined it was indeed the logic board. $571 or something. I took the computer home with me and pondered what to do. I figured I would resign myself to getting a laptop and trying to sell the G5 for a couple of bucks. But then I thought, 'Hey, they offered to fix it for free once already and they never ended up paying for the logic board, perhaps if I ask them they will extend the offer again.' So I went to The Apple Store, asked for the manager and asked, he told me to bring the computer in and he would look at the case history but he was pretty sure there was something they could do. That brings us up to now.
They have had the computer for two weeks and can't figure out what is wrong even after replacing the logic board and video card. They want to offer me the amount of money they are already into my computer for. They agreed to fix the computer for free.
