If I remember right from my automotive classes in school, the lower the 1st number is the more fluidity of the oil - the easier it is on the pump when cold. 5W-, 10w- etc. The higher the last number the "better" the oil handles high temps. That said... if your car burns oil, a thicker version (higher 1st number) might... might help with some of those leaks, maybe. I'd go with a 5W30, if it were my car, in winter, and not burning oil.
Without knowing all the details, I can only suggest that you tear it down again. when you get to the blades, make sure the teeth are lined up alternately. I'm guessing when you pulled out the paper jam, it tweeked one/both of the blades. Make sure both blades are seated in the proper position.
Do you have a way to re-melt the putty? Have the phone sitting up, so the jack opening is down, melt the putty and let it drain out. Just be careful to warm it up to the melting point of the putty, and not too hot to damage the phone.
Usually this happens when something heavy was set on top of it, damaging the LCDs. Eventually it will grow to the whole screen. IF it is covered by warranty, get it switched. If they wont cover it, break out the tool kit and get to work.