Some guesses:

1. Different CA cert bundles between windows box and AWS.
2. Connection disallowed by AWS policy.
3. Connection disallowed by Gmail policy.
4. Different versions of perl between windows box and AWS.
5. Different versions of the modules between windows box and AWS.
6. Different versions of openssl between windows box and AWS.

Personally I would try to make the connection by hand, outside of perl using openssl's handy s_client command. If that fails then you know it's nothing to do with perl.