Make sure you are logged in in iTunes, that you have a payment method registered (though podcasting is free), and that your computer is authorised for iTunes. Downloading a free app may help.
Then try signing in again in Podcasts Connect.
If you still have problems, report it to Podcasts Support. Go to Apple Podcasts Help - Podcaster Support and click the 'Contact Us' link at the bottom of the page.
Occasionally people with this problem have been unable to get through to that contact page. If so, contact Support. Don't report it as a podcasting problem - they don't handle those - but as an inability to get to the contact page. It's also been suggested that getting them to look at your Apple ID may clear matters.