Some webhosts, like Hostgator.com, run php in cgi-mode, using phpSuexec.

dotProject 2.1.1 will install and run under this setup, but you may run into an issue when clicking on the "Company" tab, or selecting "create a new Company" from the dropdown menu in the header.

Forbidden
You don't have permission to access /admin/index.php on this server.

Additionally, a 404 Not Found error was encountered while trying to use an ErrorDocument to handle the request.

The fix is to add a file called ".htaccess" to the dotproject root folder, containing the line:

SecFilterEngine off

Many thanks to simonatron for this solution.