My bathroom sink faucet is leaking and I’ve already replaced the aerator and was going to replace the seats and springs. Turned the hot water off successfully but when I tried to turn the cold water off and let the rest of the remaining water run out of the faucet, the cold water was still flowing. I have a 1/4 turn off valve and I don’t know what to do... the water doesn’t stop flowing. Any ideas as to what I should do?
It is not uncommon for the stop-valves at the wall to fail (in various ways). The 1/4 turn valves generally seem to last longer than the traditional style valves, but they fail too.
Your only option now is to turn off the water at an upstream valve and replace the stop valve. Your home should have a main shut-off, or you may have to go out to where the water is metered and turn it off there.
I encourage you to go with a 1/4 turn valve again despite the trouble you have now; try to buy a quality valve, not the cheapest one. A plumbing shop (as opposed to a "big-box" hardware store) may be a better place to purchase a good brand.