liquid damage is always a crapshoot. the good news is it doesn't look like the pee penetrated too far into the phone. the LCI (Liquid Contact Indicator) - the white oval directly above the apple logo on the battery and below the black square near the top - is still white, if liquid had reached it, it would have turned red.
for submerged phones, i usually recommend disassembling and removing the major parts (motherboard, camera, taptic, speaker, battery, etc) and treating them to a soak in 99% IPA (isopropyl alcohol) - with the exception of the rear cam and battery, those should just be wiped down with IPA. very gently use a soft bristled toothbrush to scrub away debris that may have settled on the parts. then a rinse with fresh IPA and let the parts dry in a warm environment at least overnight.
the screen is a bit trickier. you an only remove the earpiece/front-camera assembly and the back shield, the rest of the display is pretty much sealed up but if liquid got in there, it could be a problem.
to address the phone booting/non-booting issues, i recommend downloading a copy of 3utools (it's a great utility and it's free). disconnect the display from the phone, connect the base to the pc via usb and power it up. if the phone boots, 3uTools should see it and give you an summary screen, or a popup that says the phone is in recovery or DFU mode.
you'll have the option to do a flash, which installs the latest IOS, but if it's via recovery or DFU, it will probably wipe the data from the phone (hope you have a current backup).
good luck