Can a stop tap fail?

I have a problem with low water pressure/flow in my house. The problem is at
the stage that if two taps are opened at the same time, water does not flow
at all out of one tap.

Pressure in the street is OK - neighbours have no problem, and stop tap in
the street in fully on.

The stop tap in the house appears to be in the cellar (cast pipe to copper
half buried in the wall), however turning it makes no difference at all
either way. I therefore suspect that the stop tap is not for the water?

Is it possible for a tap (stop tap rather than gate valve) to fail
completly.

Any ideas what else the problem could be?