Hi Tim.
If there is significant corrosion on the module, then there is a high likelihood it's damaged beyond repair. You could try another quartz crystal (32kHz) in it, based on the symptoms you describe.
Your other options would be:
1. Get a beaten up working TC1 off Ebay and replace the module. However the magnetic reed switches may need adjusting. They tend to go for US$500-600 minimum.
2. Get a beaten up working P2 Pulsar and replace the module. Same deal with the reed switch adjustments, and also it wouldn't have the Omega logo on the module (which I think is important). You could take this option, but get someone to swap the ciruit board onto your original plastic carrier, so it's basically all original.
3. Hanno from Stikes and Spares will "fix" your module. This involves basically using your original display, plastic carrier and reed switches. This module has no trimmer, so won't run as accurately as it should. No light sensor either.
Option#2 is your bet bet if you want original. A beaten up P2 might cost US$250, and someone might swap it onto your carrier and adjust the reed switches for US$100 or so.
Hope this helps.
Rgds,
Andrew.