Cannot install Search API pages module, due to database errors?
I have had a similar issue.  I resolved it by installing search api on a fresh drupal install and exporting the databases then importing to the original database.  I would not recommend doing this first however.

First you should uncheck search api module in your modules list, then click the uninstall tab and uninstall it.  Grab a new copy of the search api module to make sure you didn't have corrupt files and install it again.  If this doesn't work, then you may want to try what I had to do.