If the code box is clearing when you hit continue but the page does not advance, there may be an option selected in your browser's cookies settings or a problem with your cookies preventing the page from advancing.
The easiest solution would be to try an alternate browser (preferably one you normally don't use), such as Firefox or Google Chrome.
You can also try clearing your cache and cookies for your current browser if you are familiar with that process. The process to clear out cookies/cache is a little different depending on your browser, but most browsers have an option in their settings options under Privacy or Content settings.
A third option is trying another device with internet access using the web browser on the other device.