The 2 ohms residual resistance seems to indicate an FPGA internal damage rather than a simple PCB short, that can be expected to show zero ohm.
There's a point in your post that seems dubious to me, although it's most likely unrelated to the discussed TCK pin failure.
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It is not a lead free board. Components are leadfree & but assembled with leaded profile.
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No chip vendor (also Altera) doesn't support processing of lead-free BGA packages with leaded solder paste. This option exists for all other package types, except such with BGA balls. The resulting non-eutectic alloy won't give reliable solder joints.