It's been a couple of days since the last post, did you figure it out yet? My guess would be that when you turned the water off just upstream of the heater, that valve, a ball vave or a gate valve, just isn't back open to full flow. The basement sink is probably upstream of both the valve (you turned off for the heater replacement) and the heater itself. I haven't seen too many ball valves fail but I can see how maybe the stem could become detatached from the ball and not open the ball. A gate valve can have several problems. The best way to install one of them is with the handle down. That way, if the stem becomes detached from the gate, you can at least push the gate closed to stop flow in an emergency. I've had one stick on the closed position and strip out and not pull the gate back open.
I wouldn't have plumed a house so that when you turn the water off to the water heater, the cold water is off to the rest of the house, but then it's any ones guess on just what happened.
Let s hear what you find.
Ernie