iPhone 5s Says "Searching" after water damage

Just my 2 cents...we do a lot of water damage at my store.

First obviously clean the main board and any connector's you see corrosion as quickly as possible with isopropyl alcohol (try 99% if you haven't already...it makes the difference).

When device is powered on, with sim card installed (active or not), toggle wifi and airplane mode in that order. If it says no service it's reading the sim card so you can rule that out. If it says no sim, toggle airplane mode again to see if it still says no sim or no service (or hopefully service :)

Once you've ruled out it detecting the sim time to move onto your antenna. Try replacing the dock connector/antenna assembly. If that doesn't work dig a little deeper. Any metal plates you can remove (and two can be lifted up with a little bit of "gentle force" do it. See if anything has been corroded or damaged.

Also try another sim card as it can be damaged easily from liquid/water.

Hopefully this helps.

As a last ditch I would soak the main board in 99% aldohol (found at Safeway) for a good hour, then scrub with soft brush like your life depends on it. A mistake I see a lot make is they don't take the time to remove removable metal plates so they're not cleaning all components (ic chips, connectors, etc) of the motherboard.

When water is spilled on a board you can not simply dry it out. The water does evaporate but leaves behind residue and corrodes parts - often not visible without a microscope. You have to clean it to get it to work properly provided the damage is minimal. Sometimes the water will damage parts that leave the device unusable without board repair/replacement.

As mentioned by @mdrecovery you can try to use alcohol. Your best option is to find someone with an ultrasonic cleaner. I agree you can remove the removable parts (which should be obvious) but do not pry or pull on anything that is soldered.