Hi,
You have a javascript issue on the page.
take.ms/degs7
When you finish the checkout, there is a little script which update a value before submitting the form ; if that value is not updated, the checkout can't finish.
So if you have some javascript issues, it's possible that the script is not called and then, the checkout can't be completed.
Your template is completely compressing the javascript on the page so it's not possible to analyse it.
Please follow the recommendations of Nicolas and try a checkout with the default template of Joomla. If that works, I would also recommend to contact your template provider for help.
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.