Vostro 1310 screen problems (red lines)

Attach an external monitor.  If the fault doesn't show there, it's a panel problem,  If it does, the video chip is faulty and you'll need a replacement system board.

This system uses a known faulty nVidia graphics chip - there's a 1-year warranty extension on that problem only:

http://en.community.dell.com/dell-blogs/b/direct2dell/archive/2008/08/18/nvidia-gpu-update-dell-to-offer-warranty-enhancement-to-all-affected-customers-worldwide.aspx

The image is perfect when i use an external RGB monitor, so I suppose -as you said- that the video card is ok, but the LCD itself is gone.

I already tried to disassemble the laptop, i am out of warranty so I have no choice, I have to do it by myself. I can't really understand if the fault is in some connection cable or in the lcd. Is there any way to buy only the lcd? Is it something that can be sold separately?

Try reseating the cable first - if that doesn't fix it, replace the cable.

If you get no effect with a new cable, it COULD  be the LCD - but I've seen these nVidia chips fail in such a way that the internal display goes bad while the external one is OK for a while before it, too, fails.