Misfire, codes PO300 and PO303

The P0303 is a specific cylinder misfire (Cylinder 3) while P0300 is a random misfire code. A common cause for the random misfire on a 5.4 is the intake manifold gaskets. They will get hardened and then they do not seal fully. The other common issue is the plastic manifold cracking on the underside. Both of these can cause a vacuum leak which causes the random misfire due to it not being air that was measured through the mass air flow meter. Usually in the case of the gaskets the engine will idle poorly while it is cold and get better as the engine warms up and the parts expand slightly and seal better. The cracked intake however usually just causes the random miss due to the lean fuel mix.
Depending on which issue you have it could also cause the P0303 code if the gasket at that cylinder is leaking more than the rest.
Easy way to test for this issue is to get a can of starting fluid. Then with the engine cold, start it and immediately spay the fluid at the area where the upper and lower intakes meet, as well as up under the intake. Any change in how the engine runs or if it suddenly revs up will point at what and where the problem is.

Water intrusion will cause a myriad of problems. Good to hear you found it. Thank you for using 2CarPros.