This looks like the output filtering on a class-D amplifier? - as suggested, the inductors don't fail - if the core is loose, just glue it (super glue works really well on ferrite).
There's pretty well nothing there which does fail - if you've got a fault, it's VERY, VERY, VERY unlikely to be found in that part of the circuit. What I would do, is bend that blackened resistor away from the capacitor, like the other ones - but both are probably OK anyway.
I would suggest you don't bother trying to test the inductor - the chances of it been faulty are pretty well zero, and the chances of you breaking it are probably well in double figures!.
What's wrong with it anyway?, and why are you suspecting these parts?.