Sounds like the blower resistor has gone bad. It's located up in the dash behind the glove box. I'm not sure if you have to take the blower housing out or not to replace it. It's about $25 from Honda. Here's where it's located and how to replace it.

http://www.honda.co.uk/owner/civicManual/pdf/21-12.pdf
http://www.honda.co.uk/owner/civicManual/pdf/21-13.pdf

Here's a pic that you can show the dealer if you need to. It's number 5 on the diagram.