The message clearly states the username and password you're using to connect at design time in your development machine are not valid to the database server you're trying to connect on the other machine (let's call it production). From your message it seems it is not the same server you connect to at design time.
I suggest you to test this issue with ease to put the LoginPrompt property to true on the TIBDatabase component to allow it to ask the user for propper credentials before connecting. You will be able to connect using any valid username/password combination for that server. To be sure the combination are valid, try to connect using the isql command line tool, for example the command
c:\test>isql test.fdb -u sysdba -p masterkey
will connect to c:\test\test.fdb using default username and password. (the firebird root directory must be in the path environment variable for this to work)
Also, you can use the gsec command line tool to adjust the password for this engine or you can provide the create users and change passwords on that production machine before trying to connect to it.
On Windows, firebird default sysdba password is masterkey.