SSL certificate issue when trying to clone Git repository within Cygwin

Question

I'm stuck behind a firewall so have to use HTTPS to access my GitHub repository. I'm using cygwin 1.7.7 on Windows XP.

I've tried setting the remote to https://[email protected]/username/ExcelANT.git, but pushing prompts for a password, but doesn't do anything once I've entered it. https://username:<password>github.com/username/ExcelANT.git and cloning the empty repo from scratch but each time it gives me the same error

error: SSL certificate problem, verify that the CA cert is OK. Details:
error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed while accessing https://github.com/username/ExcelANT.git/info/refs

Turning on GIT_CURL_VERBOSE=1 gives me

* About to connect() to github.com port 443 (#0)
* Trying 207.97.227.239... * successfully set certificate verify locations:
* CAfile: none
CApath: /usr/ssl/certs
* SSL certificate problem, verify that the CA cert is OK. Details:
error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed
* Expire cleared
* Closing connection #0
* About to connect() to github.com port 443 (#0)
* Trying 207.97.227.239... * successfully set certificate verify locations:
* CAfile: none
CApath: /usr/ssl/certs
* SSL certificate problem, verify that the CA cert is OK. Details:
error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed
* Expire cleared
* Closing connection #0
error: SSL certificate problem, verify that the CA cert is OK. Details:
error:14090086:SSL routines:SSL3_GET_SERVER_CERTIFICATE:certificate verify failed while accessing https://github.com/username/ExcelANT.git/info/refs

fatal: HTTP request failed

Is this a problem with my firewall, cygwin or what?

I hadn't set the HTTP proxy in the Git config, however it's an ISA server that needs NTLM authentication, not basic, so unless anyone knows how to force git to use NTLM, I'm scuppered.