Ok, fine - and the customer service rep suggested I try using Internet Explorer; I thought I had noticed it here on the machine already, and sure enough it is. In the interim I payed my bill via the phone call.
What I found highly entertaining was my CSR had a bit of an accent, so when she said "Internet Explorer" it honestly sounded like she was saying "Internet Exploder" instead. A perhaps unconsidered side effect of outsourcing, heh.