I would perform the usual 6 month cleaning (the one where you use CANNED AIR) on the vents and if this is many years old it's time to replace the usual compound.
Don't let your diagnosis blind you to the usual. We see such a lot in the shop as folk "prove" it's not this or that. We nod and do the cleaning and compound and you don't want to know how often that works.
I can't tell which cord you are asking about. But the cable from the mainboard to the LCD is a suspect but not high on my list.
I have a Lenovo T61. Lately, the screen will randomly become pixelated pink. I can see what's going on, but it's proving to be an annoyance and I feel something is about to go out. If you move the screen back and forth, sometimes hitting the back of it, you can find the sweet spot where it doesn't do that, but other times you can't. I know it's not a GPU problem, as hooking it up to an external TV screen for several hours works just fine. I'm not sure if it's the cable between the body and screen, because moving it around and messing with it does nothing. Just wanted your guys' opinion, as it means the difference between $5 and $35. Thanks.