I would try reinstalling WAMP or MAMP or XAMP. Usually sessions not working is an issue in your php.ini file with the session.save_path pointing to a non-existent directory or one with inadequate permissions. It will usually be set correctly by the server installer, so I'm not sure what happened. Unfortunately I'm not a server configuration expert, but if it works on the live server it must be a server configuration issue and not an issue with the php code itself.
What is the captcha issue you are having? That could be related to the session as well. Get that fixed first and post back with a detailed description of the captcha issue and I can try to help.