No, it was actually burnt where in attached to the module, and the solder was
melted to a point where the lead was floating around. This cap did have a wet
spot underneath it was well.

Is there a way to bypass this type of PIP module?

BWL wrote:

Burnt lead? If you mean it turned black, pull cap and check for leakage of
electrolyte on bottom; any caps you find like this should be replaced; also
check all over chassis looking for leaking caps; usually easy to spot on older
sets if there's any dust on boards; will leave a small "wet spot" around base
of cap...