They can fail open, or if toasted, can fail shorted.
?Regardless,
it's easy enough to replace one--and that's what I'd do anyway,
before goofing around much more.
With a small choke of this value, internal shorts are almost never
fatal. The inductance may go down, due to one of the layers of
windings getting taken out of the circuit. A short that bypasses a
majority of the windings is extremely rare.
Still, a minor short can mess things up.
--
Will