Thats an inductor, for the switchmode power supply on the front end.
If you cut off the heatshrink, you will find that it is a coil of wire wrapped around a ferrite slug. You may be able to epoxy some legs onto it and solder the remnants of the leads to them, and resolder it to the board, otherwise, get a multimeter with an inductance measurement (an electronics shop should be able to identify and sell you a replacement - its a common part).
Failing that, cut off the heatshrink unwind it, and rewind it. Its not rocket science. You need to scrape the enamel off the wires when you try to solder it, and glue it to the PCB when you fix it