reply to elanp
Re: Hot Water Runs Out Quickly: What's Wrong With My Water Heate You can also look inside by draining the tank and removing the drain fitting. If you can see the bottom of the dip tube resting on the floor of the tank (looking into the small hole left by the drain fitting, use a good, small mag light and get up close) then it's broken at the top.
If that's the case you have three choices: replace the tank (it is 12 years old), replace the dip tube (can be a bitch to get that fitting off and trying to remove it may permanently damage the tank) or feeding the inlet water into that drain fitting port. The last would be more of a plumbing project but it does work and you'll have no more dip tube issues. Your choice.
I bought a dip tube and read a bunch of articles on how to replace one, but I'm at a bit of a conundrum at the first steps. I turned the cold water off and put the temp on the lowest setting without turning off the pilot. The thing is: I tried to run hot water into the tub to empty the tank and maybe even get a hot bath out of the deal, but nothing comes out. The cold water, however, runs freely. That doesn't make sense to me. Is it safe for me to even proceed in trying to take the top off?
You're misunderstanding how the hot water system works. You need the cold water ON in order to provide the pressure for the hot water to come out of the tank.
The only way to drain the tank with the cold water OFF (i.e. without refilling the tank) is to use the drain valve on the bottom of the tank.
Hopefully you have a functioning floor drain near the tank, and a length of garden hose to get from the tank to the drain. Open a nearby hot water faucet to let air back in to the system so it will drain faster.
I'm thinking you should call a plumber, though.