I am not too sure about this but I think the wire is not fitting perfectly into the sockets. Try and use a friend's cable and see if it is working. Also, the screen power supply should not be warm. I just checked mine to be sure. Try an alternate cable and see. Also, what is a screen cap?
Babe you got new GC's and and shit when you bought your computer so I severly doubt those are the problem. Give everything a dust out, you'd be surprised how awful that stuff is. I think before you buy anything else you should test the monitor on a separate system to see whether it is the monitor or the system ( which we both doubt it is )
Your monitor is dying, your graphics card is dying, or you have a bad cable connection either at the back of the monitor, at the power source, or the cable is damaged somewhere in the middle. If it's an older iMac, they had a power supply issue that you can get fixed by taking it to an apple store/authorized repair shop, though it wouldn't likely be a power supply issue with the computer, because if it was then it would crash a lot or shut off randomly.
My top guesses would be it's the monitor dying or bad connection.
It just means the connections are loose at one end, the connectors at the end of the cable or on your computer are damaged/defective, or the cable is damaged somewhere. But it is not likely that this is a cable issue. First check the cables to make sure they're all well connected. If you have an extra VGA/DVI cable for your monitor, swap it in place of your current one. Unless your screen flashes on and off, the power cable is not the issue. If nothing changes, then connect the monitor to another computer. If the black lines still appear on the monitor, then you know the monitor is bad. If they don't appear, then it is most likely your video card/driver that is bad.
Hmm, hard to say. For trouble shooting problems, it's best to work down. Try to eliminate big problems, then work your way down. I would doubt it's your power cable/cord/box, but that could be the source. Try to replace it, but if you can't, then try other "global" outside things. Like the video cable or card. If those turn out fine, then you know the problem is with the monitor its self. And then you have to do a fair bit of techy work, since at that point, the repairs become a lot more expensive.
But from a pure guess here, I'd say the logic board of the monitor is failing, which means a lot of money. Might be easier to get a new one.