I've got a database "TEST", that I connect at address 123.45.67.89:1521.

How do you connect with it using PL/SQL Developer?

Within the "database" portion of the logon dialog box, enter //hostname.domain:port/database , inside your situation //123.45.67.89:1521/TEST - this assumes that you won't want to setup a tnsnames.ora file/entry for whatever reason.

Also make certain the firewall configurations in your server aren't obstructing port 1521.

I would suggest developing a TNSNAMES.ORA file. Out of your Oracle Client install directory, navigate to NETWORKADMIN. You might curently have personal files known as TNSNAMES.ORA, if that's the case edit it, else create it making use of your favorite text editor.

Next, simply add an entry such as this:

MYDB =
  (DESCRIPTION =
    (ADDRESS = (PROTOCOL = TCP)(HOST = 123.45.67.89)(PORT = 1521))
    (CONNECT_DATA = (SID = TEST)(SERVER = DEDICATED))
  )

You are able to change MYDB to anything you like, this is actually the identifier that programs will uses to obtain the database while using info from TNSNAMES.

Finally, login with MYDB as the database in PL/SQL Developer. It will instantly discover the connection string within the TNSNAMES.ORA.

If that doesn't work, hit Help->About then click on the icon by having an "i" inside it within the upper-lefthand corner. The 4th tab may be the "TNS Names" tab, check it to verify that it's loading the correct TNSNAMES.ORA file. If it's not, you might have multiple Oracle installations on your pc, and you will have to discover the one that's being used.