I already checked the query made for the same topic. like disabling ssl from admin backend and Outgoing Connections,web hosting company blocking in my case both above condition has been satisfied as I have disabled ssl from admin backend(for all paypal option which is being shown in admin payment method section) and regarding second currently we have already hosted magento project on same hosting server with paypal along with onestepcheckout module.
In checkout Iam using onestepcheckout module, when I checks the log file it shows with message: "exception 'Exception' with message 'PayPal NVP CURL connection error #35: SSL connect error'"
suggestion are most welcome..
Thanks
you probably run into a problem made by the recent update of Paypal, in fact they have removed the support to protocol lower than tls 1.2 for their sandboxes. You should update your curl and libcurl packages and specify the version in the magento code: CURL_SSLVERSION_TLSv1_2 (6) (http://php.net/manual/en/function.curl-setopt.php)