The SSRS Reports website security can sometimes be troublesome when first configured and trying to connect to it from a remote machine. The RSReportServer.config file has a AuthenticationType section that required attention if you are prompted for authentication when accessing the site remotely. By default you may get all 3 types, however if you are just using regular Windows authentication you should only have RSWindowsNTLM in the list. Removing the other 2 will allow you into the site, provided you have access to the database.

      <AuthenticationTypes>
             <RSWindowsNegotiate />
             <RSWindowsKerberos />
             <RSWindowsNTLM />
      </AuthenticationTypes>