You have several choices.
You can boil all media, gravel, etc. !0 minutes will do it. Clean the tank well, let it dry in the sun.
You can soak everything in bleach solution (12:1 water:bleach) 10 minutes. Use a good dechlorinator when you are done.
You can use potassium permanganate - add it until the water is purple and let the tank run for 4+ hours. If the water turns brown, add more pp until it is purple for at least 4 hours. The color can be neutralized with hydrogen peroxide.
The Ich critters are only capable of being killed when they arein a free swimming stage, not in cyst form or in a fish - and I have had some people that swear the cysts can survive pp treatment and even bleach! Because they can attach to plant leaves and dig themselves deep into a gravel base, you really need to remove all real plants, and clean/sterilize all silk/plastic plants. I would remove and boil all the gravel and hard media (ceramic cylindars, lava rock etc) no matter what other method you decide for the rest of the tank. Gravel is really tough to sterilize - there are so many nooks and crannies for nasties to hide in!
Ich life cycle can be substantially sped up with an increase in temperature. If you have no fish in the tank, you can remove the gravel, and boil it. Leave the rest of the tank alone - raise the temperature to 25C and run the tank as usual. You can feed your cycling bacteria with pure ammonia (just a few drops each day) to keep it alive. Now run the tank without fish for at least 2 weeks ( Overkill, I know but......). At 25C the ich should go through a complete life cycle twice. Add salt to the tank to the dilution of 3 teaspoons of salt per gallon of water. This should kill the nasties.
Since you are also not dealing with fish, some of the more "powerful" medications can be used fairly easily, but they may affect or kill your cycle. "Malachite Green, Formalin, Quinine (hydrochloride or sulphate) or Copper. These medications should be handled very carefully, especially Malachite Green and Formalin which are highly toxic to humans. Wear gloves, don’t breathe in the fumes, don’t get any into your eyes or on your skin. They can affect the tank’s cycle so it is wise to test the water parameters regularly during treatment. They are also not good for plants and invertebrates (e.g. snails) so remove these from the tank before treatment. Malachite Green can also stain the interior of the tank, especially the silicone sealant." -as per Koko's site - (thank you Emma!).
I am sorry about your fish.......

Edit: that is a full rolling boil for 10 minutes. Start the timer AFTER you reach a rolling boil.