IMMEDIATELY remove the immobilizer box and dry it. They can often be recovered with a careful cleaning. Search the forum for details from others doing it.
I'm not sure if he still does it, but forum member Qmulus repairs these or transfers your car's data to an undamaged box for a very reasonable price.
986 Forum - for Porsche Boxster & Cayman Owners - View Profile: Qmulus
ECU Doctors repairs them as well and has a good reputation:
https://www.ecudoctors.com/collections/porsche-boxster2000-2004#
You can buy a compatible (same year range and model as yours) set of Key Fob+Immobilizer Box+DME (engine computer) and replace what's in your car to make it work. The issue with that is that the replacement parts will not have the specific identifying information for your car which will cause problems for dealership/professional servicing.
I do have parts available that may be the correct year if needed.