I would not put my phone in rice if I dropped it in water. By putting it in a bag, you are essentially drying the water already, as for the rice it may pull some moisture from the phone, but you will end up getting rice residue inside the phone.
Regardless of the drying method used, you never want to dry the phone with water still inside, need to clean it first. Water leaves behind mineral deposits, which can also conduct electricity just like water. Essentially, if you turn it on without first cleaning it, you run the risk of short circuiting the phone.
1st Step: The best thing to do at this point and in case it ever should happen again in the future, is to remove the logic board and wash with 99% Iso Alcohol and lightly clean with an ESD safe brush, you can get it from the iFixit store online. Then let the board dry in a zip lock bag with some silica bags (the bags that come in shoes boxes and such). Then reassemble and check again.
*Sorry for all the extra text, but it's easier to clean the board up, because water residue can mess with the connectors and the "chips" on the board, which can affect your signal.
2nd Step: Change out the charging port (clean the frame under the charging port with alcohol first) to see if that will work. The iPhone 5S charging port is different, so make sure to use one from an SE. Then reassemble and check again.
3rd step: Likely to be one of several ICs on the board. Need to send to a Board Level Repair Specialist, unless you have a decent microscope, soldering tools and lot's of time and patience. If you have those, you can find videos on Youtube - iPad Rehad has videos of a bunch of different issues. Good start.
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