Can a boiler water feed / pressure relief valve be repaired?
The short answer: you should replace the relief valve.



The long answer: In general, you should not attempt to repair any pressure relief valve. This valve is the only over-pressure safety in the system.  This should only open if there is a blockage in the system (causing a pressure buildup), or if filling the system with a faulty pressure reducing valve.

Normally these valves fail due to calcium build up on the interior, which is hard to avoid without having a water softening system installed.

I would recommend changing out both the pressure relief valve, and the pressure reducing valve, as it appears to have quite a bit of calcium build up as well (and may have a small leak). To have both replaced would generally cost in the range of $200 to $500, depending if you replaced them yourself or not.  If there are no other leaks or issues with the system, changing both of these valves will solve your zero-pressure issue.