Welcome to ETO, kbrooky!
First thing is to carefully clean the PCB traces with some "Contact Cleaner" (or at the least, distilled water) and a soft bristle brush to get rid of any remaining corrosion and the acid causing it. Hopefully the areas you've already scrapped still have some copper cladding left on the PCB. Dry completely.
Whatever non-corroded good traces that are left will be a dull gray (solder covered). You should "jumper" over the green, corroded portions (as suggested by Diver) with a small, insulated wire that is soldered to the good (gray) section(s).
Also check for corrosion on the underside of the battery holders.
If, however, any of the green traces disappear beneath the black "glob" (the IC - the LED's flashing timer) with NO copper visible after cleaning, then the unit is toast.