Hi fanny,
Sorry for the database issues you’ve faced, I’m going to try my best to try to help you out!
The issue you encountered tends to happen when MySQL is shutdown improperly. This can happen due to a power or battery issue like you encountered, or a number of other situations. The good news is depending on the type of database tables all might not be lost.
Could you try starting one of the broken sites, then copying Local’s logs to a forum post? More details on how to do this can be found here: How do I retrieve Local's log file?
This will help us determine what the best next step would be. Thanks!