I don't understand what PKE valence is, and what it means to "take PKE valences".
"PKE valence" is technobabble - something the writers made up to sound smart and scientific, but is actually nonsensical. Valence is an actual scientific term but makes no sense in this context. In any case, we're meant to infer that "PKE valence" is some sort of measurement of paranormal activity. "Taking PKE valence" is simply shorthand for "taking measurements of PKE valence levels".
Then I don't quite get the meaning of the expression "buried the needle".
"Buried the needle" means the same thing as the previous line, "went right off the top of the scale". Presumably, the device they used to measure the PKE valence had a dial like this, with a needle indicating how high the valence was:
A reading "right off the top of the scale" would "bury the needle" on the extreme right end of the dial, and would indicate a reading too high for the device to actually measure (which, generally speaking, is a bad thing).
Does "We're close on this one" mean some kind of a scientific discovery or a Nobel prize?
Yes. It means they're close to actually discovering a real ghost, something they have apparently failed to do up to this point, as suggested by Peter a few seconds later:
As a friend I have to tell you: you've finally gone round the bend on this ghost business. You guys have been running your ass off meeting and greeting every schizo in the five boroughs who says he has a paranormal experience. What have you seen?