Hey Guys,
Sorry for the late reply!
9743Keith - Posts above have some helpful tips on how to bulk delete but failing this, give us a call. We do have a way to fully clear an inbox for you.
Smg1 - I don't believe you can close/delete your email address online. If you call on 133933 or speak to LiveChat: http://tel.st/gq6m and they can see if this can be done for you. Main emails associated to your BigPond service cannot be deleted however.
Evasolo - Have you tried using your email on the link provided above? (https://webmail.bigpond.com/webedge/do/oldlogin) This is usually a handy alternative to use when MyConnect doesn't work correctly.
Brodie