I, too, use godaddy, and I am getting the same problem (reported to me today by a would-have-been-customer).
I called godaddy, and they had no idea what was going on, and I found this thread while on hold with them...
FYI, I received an email from godaddy a day or so ago stating something about that due to security vulnerability they were changing something about my security cerfiticate.
I followed the fix listed in this thread, but it did not fix the issue, but at least now I can run the curltester:
Testing communications to various destinations. This is a simple diagnostic to determine whether your server can connect to common destinations.
For advanced "details" mode, add ?details=on to the URL.
Connecting to Zen Cart Support Server (http) ...
GOOD: CURL Connection successful.
Connecting to Zen Cart Support Server (https) ...
Error 77: error setting certificate verify locations: CAfile: /etc/pki/tls/certs/ca-bundle.crt CApath: none
Connecting to USPS (port 80)...
GOOD: CURL Connection successful.
Connecting to USPS Test/Staging/Sandbox Server (port 80)...
GOOD: CURL Connection successful.
Connecting to UPS (port 80)...
GOOD: Socket established
Connecting to FedEx (port 80)...
GOOD: Socket established
Connecting to PayPal IPN (port 443)...
GOOD: Socket established
Connecting to PayPal Express/Pro Server ...
Error 77: error setting certificate verify locations: CAfile: /etc/pki/tls/certs/ca-bundle.crt CApath: none
Connecting to PayPal Express/Pro Sandbox ...
Error 77: error setting certificate verify locations: CAfile: /etc/pki/tls/certs/ca-bundle.crt CApath: none
Connecting to PayPal Payflowpro Server ...
Error 77: error setting certificate verify locations: CAfile: /etc/pki/tls/certs/ca-bundle.crt CApath: none
Connecting to AuthorizeNet Production Server ...
Error 77: error setting certificate verify locations: CAfile: /etc/pki/tls/certs/ca-bundle.crt CApath: none
Connecting to AuthorizeNet Developer/Sandbox Server ...
Error 77: error setting certificate verify locations: CAfile: /etc/pki/tls/certs/ca-bundle.crt CApath: none
Connecting to LinkPointAPI server (port 1129)...
Error 28: Connection timed out after 5000 milliseconds
Testing completed. See results above.
====================
I do see that there are multiple .htaccess files... is the fix to go and try to find all of them and edit all of them???
Any godaddy clients like myself get the issue completely fixed yet?
Zen Cart 1.5.3, Database Patch Level: 1.5.3
Server OS: Linux 2.6.32, Database: MySQL 5.5.41
HTTP Server: Apache, PHP Version: 5.4.37