Trying to get a localhost copy working
Are you using any Drupal performance optimizations on the site that's the source of your imported database? This article suggests turning them off and gives a query to accomplish that.

Once you've got your local site up and running, I also suggest trying the Backup and Migrate module to manage your data migration. You can create a backup profile that omits your live server's cache data, which makes for a smaller backup file and may mitigate the problem you're having now.