This is an old problem with sql2000 too: restoring a database on a different instance, logins to database become invalid.

The solution is create login on the restoring instance with the same sid of the source instance

See here: http://msdn.microsoft.com/en-us/library/ms189751.aspx

CREATE LOGIN loginName { WITH <option_list1> | FROM <sources> }

<option_list1> ::=

PASSWORD = { 'password' | hashed_password HASHED } [ MUST_CHANGE ]

[ , <option_list2> [ ,... ] ]

<option_list2> ::=

SID = sid | DEFAULT_DATABASE = database

| DEFAULT_LANGUAGE = language

| CHECK_EXPIRATION = { ON | OFF}

| CHECK_POLICY = { ON | OFF}

| CREDENTIAL = credential_name

<sources> ::=

WINDOWS [ WITH <windows_options>[ ,... ] ]

| CERTIFICATE certname

| ASYMMETRIC KEY asym_key_name

<windows_options> ::=

DEFAULT_DATABASE = database

| DEFAULT_LANGUAGE = language