Don't just rely on your tap knob simply because it is able to turn, ( turning with some resistance and not the cap just spinning on splined spindle) internally the washer can dislodge in some peculiar way or manner that not even a single drop of water under mains pressure can flow through, this ios from my 1st hand experience on this, I opened the tap and found the black rubber washer dislodged and swollen, so put in a new 1/2" washer all was well for about 3 months and the same thing happened again, not a drop would come out, so I let it go for about 6 months, we simply didn't use our cold water tap and always used the hot water tap, but then just last month I felt inclined to fix it again, and same thing was found again, the black washer had dislodged and how it blocks cold water flowing through defies logic but it does. so it may also be worth checking that.
Edit....gigz beat me to it! well done gigz