Why won't my cold water line to fridge work?
 

My house had a copper water line running from a T-handle valve, piercing one of the cold water lines, and running under the house to the fridge location. I just bought the house, and the line and T-valve were there already.

Seems simple enough and straightforward. I can easily see the T-valve and it doesn't look terribly corroded or rusted.

Yet when I open the valve all the way, no water from the cold water line comes out the end of the copper pipe. :(

Did I mention my house's plumbing is old galvanized 1946 pipes? Can't understand what the problem would be unless the T-valve is clogged from pipe corrosion. But then, I would at least expect some water dribble out of the copper pipe. But I'm getting nothing, even when I turn on something that uses the same cold water line that the T-valve is piercing. Water comes out fine there.

Can someone offer advice? Thanks!

The lack of dribble indicates a really clogged tap and/or line that will require cleaning or replacing.

Self piercing valves only make a very small hole. With galvanized pipes, it probably clogged quickly. Turn off the water supply and disassemble the valve from the pipe, cleanout the hole (may take a small drill bit) and reattach the valve. I hate these valves and always install a tee and shutoff valve.