Definitely a surface-mount inductor. Is that apparent chip in the ~far side smooth or rough? If rough, this may change its value slightly as the core will distort the field and decrease the efficiency (increase the thermal losses). Also, you really want to find that chip, if there is one still floating about, before it shorts something.
Most likely, this was part of the back-light power circuit. It could be from a surge-resist section of something else, or a power conversion thingy, but I'm betting on the back-light. If the pads are torn off of the board, you may still be able to save it by soldering a very fine wire onto each lead coming to their former location and running them to the pads on the part, while glueing the part upside down onto the board with epoxy or such (leaving it just a bit above the board for insulation in case a trace runs too close). A good photo of the board should allow you to find where it came from and the condition of the site and pads. Do look around to se if it dented anything while rattling about.
(no subject)
Most likely, this was part of the back-light power circuit. It could be from a surge-resist section of something else, or a power conversion thingy, but I'm betting on the back-light. If the pads are torn off of the board, you may still be able to save it by soldering a very fine wire onto each lead coming to their former location and running them to the pads on the part, while glueing the part upside down onto the board with epoxy or such (leaving it just a bit above the board for insulation in case a trace runs too close). A good photo of the board should allow you to find where it came from and the condition of the site and pads. Do look around to se if it dented anything while rattling about.
Good luck ;-)