I have added my test user by using powershell to Reader group (New-SPUser) When I try "Sign in as different user" the login dialog pops up three time and then it will be an empty page nothing no access denied and no error.
You probably added a wrong user or password, and after 3 times trying a wrong psw or user name it will redirect you to nothing.
Check if your powershell script was correct, with user name and psw check if the domain name when you try to login is correct.
Verify the user in the active directory.
I'm sure something wrong with the user.
btw, you only get "access deinied", when the user exists and it doesn't have access to a paticular site.