Could a bad DVI cable actually mess up my GPU?

I used to use a Nvidia gt 220, and when I used vga it wouldn't let me pick the right resolution, so I used a DVI cable from my friends house and I got the right resolution but there was green pixels all over the place (I now know that was because that DVI cable was bad), so I ordered a Radeon 7770 and with that same DVI cable about half the green pixels went away and when my new cable came (a Dell branded one I got for $3 from Amazon), about 90% of what was left went away.

Maybe I'm going crazy but now I think that they're starting to get worse again (it was a $3 dollar cable I guess I wouldn't be to supprised if it was going bad already), and when I was first reading that the green pixels were caused by a bad cable, or a bad port, I also heard that it could even damage your ports on you monitor, and your GPU.

So now I'm worried, is it really possible for my new DVI cable to damage my monitor, or what I care more about, my brand new 4 day old GPU? Or is it more likely that the port on the monitor isn't the greatest anymore, the monitor's a few years old now, it has a sticker for Windows Vista on it. I like using DVI, I think text espically looks sharper, but if it could damage my new card I'll switch to an adapter and a vga cable tommorow!