Hi,
For the problem into Joomla, I think it's a problem related with the password.
We have some thread talking about it but the best forum for this kind of problem is the Joomla forum itself.
About HikaShop. You can easily migrate your store from one website to another by copying the database (the hikashop tables) and the overrides for your views (which are in the template folder, following the Joomla override way).
The best is to install HikaShop into the new website and after copying the tables and the files.
But I think that you can repair your website by fixing the authentication configuration.
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.