From a quick google search I did, this seems to be a GoDaddy server issue.
Below you will find some troubleshooting steps, copied from a similar thread in joomla.org forum.
1) From the Joomla Control Panel go to "global setting" and under the Site Tab turn off SEF and Apache ("Use URL rewriting" for 1.7 users).
2) Now move your .htaccess file to your computer via FTP if you don't have this file move htaccess.txt to your pc and open the file.
3) Remove any #'s if any from RewriteEngine On and RewriteBase /
Note: if your site is on a sub-directory the above should appear like this
4) Search for Options +FollowSymLinks and add the below right after it.
5) Save the file and move it back to your server. *If the file was originally named htaccess.txt rename it to .htaccess and then move it back to the server.
6) Turn on SEF and Apache ("Use URL rewriting" for 1.7 users)
7) Now Check to see if it is working. If it still isn't working or its happening less frequently move on to step 8.
In your Joomla root directory look for "php.ini" and rename it "php5.ini" (no quotes). If the file does not exist on your local computer open notepad if it does test again to see if it works. If it doesn't proceed to step 9.
9) Move the new php5.ini file to your computer (if it didn't exist keep notepad open)
10) Add this line, "cgi.fix_pathinfo = 1" (no quotes), to the document and save the file by going to File -> Save As -> under Save as type change it to All Files -> Change the file name to php5.ini if it isn't already named that.
Note: You may also want to add the below to the document to change your
max doc upload to joomla (you may edit it as needed).
cgi.fix_pathinfo = 1
memory_limit = 50M
post_max_size = 10M
file_uploads = On
upload_max_filesize = 10M
upload_tmp_dir = /home/content/55/6067155/html/tmp
11) Check your site thoroughly again before moving on to the last step which solved my problem.
12) Login to your Godaddy Account. Go to your hosting account.
Go to Settings > File Extensions Management
and edit .php and .php5 from "PHP5.2xFastCGI" to "PHP5.2X"
13) Test out your site if this still doesn't work Contact GoDaddy and make sure you send them all of the above information because you may have a server issue.
Also check this question: « Joomla “No input file specified” on GoDaddy server » in SO