Problem with display on recently bought PowerBook

Hey. I'm a brand new poster here with some pretty bizarre problems with my new powerbook.
I think I have a pretty unique problem which I havent been able to get any information on. It seems that when I tunr the thing on, little groups of short veritcal lines start appearing on the display. Eventually it gets so bad that I can't even read the thing and I need to restart.
The weird part is that it seems to start as soon as I turn it on. I can see lines even on the grey apple screen. Lines also form on the external display I use. I can't imagine how this would be a software problem since it happens before the os even starts up.
However, this doesn't happen all the time, either. I turned it on once after I noticed the problem and the thing looked fine the whole hour or so I was using it. After I put it to sleep and reopened it, the problem was there again.
This problem doesnt affect any real usage of the computer, however. In fact, I'm typing this post on it right now (it is a little hard to read though).
I tried rebooting as well as resetting the PRAM, but no luck. I also called Apple who didn't have much information.

This computer is 3 weeks old. I'm going to get a Genius appointment at my Apple Store hopefully on Monday, unless somebody has any information on this. This leads me to my next question: Will Apple replace the thing for free? And since I paid $2500 for this, will they reimburse me the whole amount, or will I just get the new 15" that retails for $2000? (i.e. Do you think it's possible for me to get a RAM upgrade/new iPod/whatever else will bring the total to $2500.

I have a screenshot if anyone would like to see it.

Thanks.

P.S. Here's the specs:

15" 1.67 GHz Powerbook G4 running Tiger 10.4.2
512MB RAM
128MB VRAM
SuperDrive
etc. etc.

 

Screenshot

Here's the screenshot... Any ideas?