Also, what should I expect to pay for a new water heater (with installation) if this doesn't work.

Thanks for your help!

Sediment buildup can lead to it not working efficiently.

Cost can vary depending on what has to be done. If you are in a fairly new house then the labor should be straightforward and vary depending on if it is in the attic or not.

If it is an older house and your city has changed the codes then your cost can go up.
I had mine replaced under the home warranty and should have been out the $50 charge. Little did I know that in the peoples republic of Austin it required:
A permit
A drain line installed from the pan, through the wall and down to the lowest level of my garage floor. (it couldn't be tied into my condensate drain line for the AC that was 1 foot away)
A new gas fitting with the trap for any particles
A new double walled vent pipe
3 vacuum breakers for my outside faucets
and a home inspector to come out and sign off on all of it as well as to make sure I have a smoke detector within 10 (or so) feet on any bedrooms.

So giving a proper estimate on labor will depend on a lot of different things.