Object Fix Zip is a free tool which can try to recover corrupt, damaged or partially downloaded ZIP archives. The program is constructed as a wizard, which makes it very straightforward to use. Add the files you’d like to repair in one step, choose the actions you’d like to carry out in the next.
It should be able to help with most problems. It can test an archive to confirm the nature of any corruption, for instance. There are options to create a good ZIP file from the broken one, or, if that’s not possible, to at least recover as many files as it can. And it can work with password protected archives.
Object Fix Zip may not be quite as effective as the authors claim, then. But as they’re giving it away for free, it’s hard to complain too much, and certainly you’ve nothing to lose by giving it a try it just might be the tool you need to make a broken ZIP file readable again.