I couldn't get this to work either on Godaddy. Everything uploaded ok to the site using FileZilla (tried it twice) and the install would go smoothly until creating the admin account. Then the install bombed with the "No input file specified." error and there was no user in the lime_users db table.
I also would get the error when I attempted to navigate to /limesurvey/index.php/admin/.
I searched the forums and
found a thread saying that FastCGI was to blame. After much frustration, I finally caved and changed the option: Hosting -> File Extensions Management -> .php extension changed from "PHP 5.3.x FastCGI" to "PHP 5.2.x". I deleted limesurvey/application/config, dropped all the tables in my DB, and went to /limesurvey/index.php/installer/welcome. This time, the installer worked and I was able to login.
I can currently reproduce the issue on the site by changing the file extension option and attempting to navigate to /limesurvey/index.php/admin. Is there anymore information I can provide in order to troubleshoot?