No hot water but cold water is fine?

So the plumber that installed the new water heater didn't check to make sure you had water flowing in both lines before leaving?? Not much of a plumber. Having the lines blown out with a compressor shouldn't be that expensive, especially if it's just the hot water side. Probably cost less than $200. It's not that complicated a procedure.

The problem is most likely within the first foot of piping on the hot water out pipe that comes out the top of the water heater. It is very likely a bad emergency shutoff valve. Clogs tend to form at valves because they are a restrictive orifice, and debris gets stuck there. In the old days they used gate valves for the shutoff valve at the water heater. These typically get stuck shut and the connecting shaft breaks off internally. When you hire the plumber, he should start with checking the nipple on the water heater, then the connector flex, then the shutoff valve, then the first nipple before it penetrates the wall (and the first elbow if there is one. Most likely the problem is in this area. If so, you should only be paying for an hour or so of labor and some cheap parts. If the problem is inside the wall, then you may have some big costs. However, before you tear into any walls, double check the isolation valves at all the faucets to make sure they are open and not clogged. The previous owner may have shut them off since the water heater was bad. If they are open and there is no flow they are still high priority suspects for clogging. When I renovate, I replace ALL The shutoff (isolation) valves with 1/4 turn ball type. They are less prone to clogging, require less maintenance, and are less prone to failure in an emergency. Replacing them is cheap insurance.

I would first want to locate the clog buy simply opening the drain faucet at the bottom of the tank if water runs ok then the cold line going in is ok then i would try to use water pressure from the cold side using a garden hose connected to the hose of the hot faucet on the clothes washer then disconnect the hot line going out of the tank and back flush the line if its still clogged id buy a compressor and blow it out and keep the compressor for many other uses

first check for pressure the tank should have a blow off valve on the side or top lift it up .if you have water shooting out you have pressure if not the cold water shutoff is closed.if you have pressure check the hot water line to see if there is a shutoff that is closed. make sure the hot is not turned off at the sinks. if there is a plug you would not have to replace all of the pipes. shut the water off at the tank if gas turn it down to pilot if electric shut off the power. go as far as you can along the pipe cut the pipe turn on water if no water you know where the plug is.(you don't need to solder it get a solderless connector lowes has them) if you have water run a snake up the pipe toward the sinks.