They are usually either a very obvious socket and plug (did you check
both ends of the cable to see which end disconnects? or a 'slide-in'
fit, with a very thin, flat 'plug' that is merely thick plastic with
the contacts porinted on either side.  The latter is easily damaged, be
careful.

Now that you can see it (and presumably it's part number), you could
always order a new one and wait to get it - once you see the
replacement LCD, it will be obvious..  That's if you haven't died of
shock as to how much it costs..