Hi! The lines are just a defect in the screen, and unfortunately there's no real fix.
As for the video problem that is resolved by pressing to the left of the trackpad, it's not the ribbon cable. But congratulations, you do have the infamous iBook G3 video issue! :-) Basically what's going on is that the solder connections on the video chip on the underside of the motherboard are coming apart, so when you apply pressure, the connections touch and it works, and when you release it, they eventually get separated again and the screen goes black. So the screen itself is not the problem, although many people mis-diagnose this issue and try replacing the screen, which is of course pointless. And then they leave half the screen screws out, which eventually puts too much pressure on the screen hinge and causes it to break at the base, etc. etc. etc.
There is no permanent fix for this issue, unless you happen to be insanely good at soldering. I've had some success using a heatgun to heat up the chip and let the solder melt, re-attaching the connections. However, it's hit or miss, and if you miss, likely you'll permanently damage the board.
The other method is the "shimm" method, which involves placing a flat object between the lower case and the video chip, constantly applying the necessary pressure. For this I use a very thin piece of cardboard, and wrap it in tinfoil so that it's not a fire hazard. Eventually it gets used to the shimm and requires something thicker, but the laptop can end up working for a time, especially if its not moved around much.
Anyway, I hope that helps! There are videos on YouTube if you want to see where the video chip is, etc. I try to identify "video issue" machines and avoid purchasing them, or else buy them for $20 and use them for parts.