how do you know a login failed in the first place from a client app? Depending on what alerts/logs you have set up you could check the sql server error log. You could also check the server eventvwr application log
And check the master.dbo.sysxlogins since you mentioned sql2000, but it will not show the db they tried to connect to. it will show you their status.
you could run the sp_helplogins proc too to get syxlogins information.