Exactly how do you know that the info and billing e-mail addresses don't work? Is it just because you haven't got an answer or do you get an "unsuccessful delivery" message from a postmaster in between? For the first scenario you've already been answered, they're on holiday.
For the second scenario, try the support address and if that too bounces back there's an issue between your provider and theirs. There's often some error code and explanation in the "could not send" error message. At the simplest it might just be a typo, a comma instead of a dot, or that you have accidentally blacklisted their domain so look at the junk mail rules of your e-mail program. Also, if you're using an e-mail program, you can try using sending from your webmail to find out if it's in your program settings. If that's not the culprit, your ISP might have HTC blacklisted for any odd reason, even vandalism. There's multiple variables in the path.
