My phone won't charge, neither play sound via speaker

Hi Alex. Water damage is very insidious. It creeps underneath IC's and can wreak havoc unseen to our prying eyes. It is the most difficult repair to troubleshoot. Here are some pointers to get you going:

1. Before you clean anything, observe where the water damage (corrosion) is occurring and look up that area in the schematics to see what it controls. The root problem can always be elsewhere but it's a good place to start.
2. If you are comfortable with a multimeter, you will need very sharp and pointy probes. Some people affix needles to their regular probes. Look up and locate an iPhone 4S schematic, they are available in the wild.
3. Generally speaking, water inside an electronic circuit will short a power rail (or more than one). An iPhone has dozens of power rails powering various functions. They are all filtered to various extents by capacitors. Capacitors are the component most likely to fail or be shorted. Then there are the IC's which can be damaged by the high current draw of a short.
4. As for inductors, the small tiny ones, like L3 & L4 on your linked article, do act as fuses so certainly check those. The larger ones, coils, tend not to go bad because they are essentially coiled wire.

In your case, I would focus on U5 (the PMIC, or power supply chip), U60 (Audio chip) and U702 (Speaker amp). Make sure they receive the voltage rails they need to properly function (such as PP1V8, PP_BATT_VCC & PP1V7_VA_VCP which are generated by U5).