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Likely just the start device, the compressor is a sealed unit so the water would not have affected it.
Here's what I'd suggest you try...
If you feel like you can trouble shoot further I`ve provided the following info to assist you or you may decide to call a professional appliance technician as I would suggest.
I don`t know the age of your fridge, but I should mention...** Most of the manufacturers of fridges have 5 to 10 years sealed system warranty which would include the compressor but not the electrical starting devices i.e., the overload & relay. Check your owners manual, it is the ultimate authority on warranty no matter what anyone else tells you according to.**
If you have a multi- meter you can check the compressor to see if the windings are ok.
**First, Unplug the fridge**
Remove the panel at the back down at the bottom. This should gain you access to the compressor.
On the side of the compressor will be the start relay/overload assembly such as this image...it may be enclosed in a black plastic cover as well.
Pull off the relay & overload and you'll see 3 pins in the form of a triangle...
With a meter measure between any 2 pins at one time, going between each pin with one remaining on a "common" pin.
You'll want 3 measurement's, similar to this example- 6ohms, 3ohms, and 9ohms.
On some meters you may simply get a reading of "0" ohms, as long as the needle moves off of "infinity" which would indicate an "open" winding=not good !
If following that, the readings are good, purchase a hard start kit. Part # HS410 also known as a 3in1 starter kit.
The above package contains info and hardware on how to connect it. NOTE : the HS410 ( 3 in 1 ) should be considered just a temporary "fix" as opposed to an actual "repair" in should not be relied on for long term reliability or safety, but rather thefactory replacemnet, double check with your model number. Hope that help`s move you forward if nothing else. If so please take a second and rate the reply and a testimony to your inquiry you received here at FixYa.
Thank you and good luck.