Upon doing so, I found my account privileges were set to trial ("Trial accounts cannot post," etc.)
I submitted a support ticket.
Now I feel dumb--the situation resolved itself (since the Blizzard agent reported there was nothing that could be done from his end). Seems like a processing delay (charging of credit card, or something).
Perhaps a little notice before you purchase, something like "Processing of your purchase may temporarily affect your account privileges--please check back in a few hours before submitting a support ticket" would prevent people like me from being confused by this.