I managed to fix it. I ripped out the mainboard and then submerged the power button in 90% Isopropyl Alcohol for about 2 minutes to remove the corrosion and repeatedly pressed the power button while submerged. Then I used a CO2 can to blow the alcohol back out. Took 2 days to dry because the alcohol got between the screen and digitizer, but it started working again. So far, no problems.
Not that I would advise anyone else to try it, but the phone was basically useless as it was prior to the fix.