Windows domain group authentication failed

I have created a dmoan called prodappaccess and added my prod
amesh id to the group prodappaccess. the group prodappaccess has been added to the sql server with db access.
i have logged in to the server but not able to connect SQL server, becuase my authenication has been failed.
SQL Version: 7 standard edition
user name: prodappaccess
DB access : public and some db access
prodappaccess - Windows domain group
some one please let me know resolution.

is sql server member of the domain.?