This has been a problem for some people. You must have a payment method registered in Apple Music/iTunes: make sure your computer is authorised to play purchases (Apple Music or iTunes menu Account>Authorisations>Authorise this Computer). Then try logging in at https://podcastsconnect.apple.com
If this fails I would suggest reporting it Podcasts Support: iTunes Connect | Contact Us
If that fails the next step is to contact Apple Support: Support
Don't present this as a podcasting problem - they don't handle those and will refer you to Podcasts Support (or give you an inaccurate answer judging by some people's experience). Present the problem as being the inability to access Podcasts Support. It's also been suggested that getting them to look at your Apple ID may clear matters: do you have a Developer ID? Someone else found that his didn't work and when he created a normal ID it worked.