In all likelihood, yeah, sounds like that, in which case we'll replace it. If we can do a little diagnostics first though...
That one pixel that works: does the color 'make sense' with what's on the screen, or is it just flailing random colors?
Also, if you wouldn't mind moving the data and clock wires to pins 2 and 3 and running the strandtest code mentioned here
, that'll test it out in a simpler configuration with fewer places to go awry.
So yes, may just be a dodgy connection in the first or second pixel. Give the plastic capsule a firm squeeze against the circuit board, see if it starts to behave. If so, with a little Dremeling and soldering it may be recoverable, or if you're in no hurry we'll simply swap the strand.