Can you install other plugins or is it just this plugin? If you can install others it's not the server.
I would then look at the zip file and extract it. Many times premium themes and plugins have a zip file that provides all the documentation and files -- AND the actual install zip within. If you try to install the main zip it will fail.
If neither of the above issues are the case, you have to then contact GoDaddy support to find out what is happening on the server side.
Good advice from @Muse. In addition to her suggestions, make sure you have enough resources for your installation. You may need to increase memory and some php parameters. Here are the wp-config files and .user.ini files that I often use on larger wp installations.
memory_limit = 4096M
max_execution_time = 320
max_input_time = 240
post_max_size = 120M
max_input_vars = 2000
file_uploads = 6
max_file_uploads = 20
upload_max_filesize = 100M
add the line below - usually I put it just above the define (db-------) (around line 20)
define( 'WP_MEMORY_LIMIT', '4096M' );
Hope this helps,