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If it is a case of a bad 'immobilizer box' there are a variety of solutions.
- ECUDoctors.com has been repairing these for years. There are also some vendors on eBay that offer repair service.
- Buy a good immobilizer box and have the chip with the car's data transferred from the corroded board.
- Buy a complete matching set of immobilizer box + key transponder + DME from a similar year and model car and swap it all in.
- Spend more than you paid for the car for a dealership to repair it.
- * I'm pretty sure that 'Qmulus' who has been mentioned in many related threads is fully retired now and no longer repairs these.
If battery power was applied for a long time with the immobilizer box corroded, it may have damaged some of the wires that connect to it. Inspect them and clean all the connectors.
Along with a bad rear window, the problem is often clogged drains beside the engine compartment.
Clean your drains regularly so it doesn't happen again.
https://986forum.com/forums/boxster-general-discussions/73399-blocked-convertible-drain.html
https://986forum.com/forums/diy-project-guides/64615-water-battery-area-1999-boxster.html