If someone turns their water main off to work on a plumbing and toilet problem, why would the cold water come on but no hot water. It doesn't come out at all or it will drip.
Why would this be, and how can I fix it?
Since you have no water coming out or just a drip a large chunk of rust or scale could have broken loose from your main and plugged the water heater. I would close and open the valve to the water heater to see if this crumbles or breaks up the debris. If that works it really is time to flush the water heater from the bottom drain. A hose connected to the bottom drain and taken outside or to a close sink or toilet makes this job clean and easy. If you have valves on both the inlet and outlet cycle both. If this works on the outlet side be prepared to clean the faucet aerators. If you get water running and hot water again it is also time to check the Anode rod. Anodes reduce corrosion inside the water heater and are eaten away (Another source of gunk in the bottom of the tank). Good Luck.
You have to be aware of without knowing the age and condition of water heater it's hard to say. What most people don't know is that every year you should drain your hot water tank. This removes all the rust, silt and sediment that settles in the bottom of the tank. If you're like most of us, and you don't do that yearly then you almost always shortening the life of water heater. If you have ever seen a water heater cut in half after just 5 years of use you would most likely not want to drink anything coming out of that water heater. Just google it ...
My recommendations is to check the pilot light first if gas water heater or electrical panel for electric water heater to see if it something very simple to fix. If not call a licensed HVAC/plumber to help you out.
Please also drain it. That is what the large spigot coming off bottom side of it is used for. Just hook up your garden hose up to it and turn it on. You might be surprised of what comes out the other end once it gets to the bottom. If clean when completely emptied then your done.If not let it feel up again and empty.