Hi,
When you are not logged, the "next" button is hidden by the "login / registration" module.
As you can see in your checkout you have a "register" button in order to create a new (guest) account.
Once logged with a Joomla account (or an HikaShop guest account), you will have your "next" button.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.