This page addresses archive extraction issues. If you have gone through the extraction and have a problem restoring your site (e.g. an error about sessions, database restoration problems, site setup issues etc) you are on the wrong page. Look further ahead, at the ANGIE section.
First make sure that your hosting environment complies with the minimum requirements for Kickstart. If your host is using an older version of PHP as the default (which might be different than the one reported in your hosting control panel) you need to contact your host to find out how to upgrade PHP on your server.
If the extraction process does not start, i.e. you click on the button and nothing happens, please go through the client-side troubleshooting steps before doing anything else. Most likely it's an issue with your PC configuration or ISP. We won't be able to help you if you don't go through these steps!
If nothing of the above works, you may want to try downloading the latest version of Kickstart, extract the ZIP file locally and re-upload kickstart.php to your site.