It looks like a common mode filter to me, VERY common on most things with a switchmode supply (computer, monitor, printer, PVR/VCR, etc, etc)
They prevent (or at least reduce by a large margin) khz-area noise from being induced into the mains (house) wiring.
From "Switching power supplies 101" a few years back:
In some rare cases, you'll also see them in linear supply equipped equipment too.
The 80's era Fluke bench mounted mains powered multimeters were one example.
They all do the same thing - stop any garbage leaving the thing via its mains cord.
With this coil removed and the connections bridged with wire the FC works correctly.
Therefore, the equipment will work OK, but may radiate or induce some noise.
I would like to replace this Coil but cannot identify it.
Raid a discarded AT or ATX computer power supply (follow the 240V feed to the PCB to find the right coil, it will connect in most cases to active and neutral).
Or raid a discarded PC monitor / DVD player / VCR / or a facsimile thereof.
Cheers from down under...
PS: still looking at that crowbar issue, it'll have to wait until I can build one here to try and replicate your problem...