Hi,
I see that the joomla login page doesn't work either so it's not a problem related to HikaShop since HikaShop has no role in the login of the user on the Joomla user login page.
Turning on or off the redirect Joomla registration to HikaShop plugin won't help. That plugin's role is to redirect to the HikaShop registration page when the customers try to display the Joomla registration page. It doesn't change anything for user login so it is a pure coincidence if you were able to login after turning it off.
A few advices here:
1. There is no error message when you try to login and it fails. There should be one, which would help you understand why this is happening. So it could be that your Joomla template is not displaying error messages:
www.hikashop.com/support/support/documen...tibility-issues.html
You can also temporarily switch to the default protostar template in order to see if you get an error message displayed when you try to login.
2. If the login works for some users and not others, then it means that these users probably don't have the right to login. Make sure that your test user is in the "registered" user group when you edit it via the Joomla user manager, and make sure that the "registered" user group has the access right to login to the frontend (that's a setting of the permissions tab of the Joomla configuration).
docs.joomla.org/Help25:Site_Global_Configuration#Permissions
3. It could be that some authentication plugins are disabled in the Joomla plugins manager, so check there too.
4. Create a thread on forum.joomla.org for your issue. Maybe someone else already had such issue have a Joomla 2.5->3.x migration and will know the solution there.