You could try & see if the Combo 10.4.11 Update for Tiger could supply
a workable fix where the Terminal application is otherwise missing. Not
sure what options exist; nor how to restore a seldom-used system part
except through an official Tiger install disc. ~ Or by use of copy-Clone.
There should be links to Apple support Combo update (PPC or Intel)
10.4.11 for PPC or Intel = Updates Mac OS X 10.4 to Mac OS X 10.4.11
(from here: http://www.thexlab.com/faqs/macosxupdates.html )
This may or may not cure anything: to try PPC Combo 10.4.11 version:
https://support.apple.com/kb/DL170
I've never heard of a Terminal application or utility gone missing in OS X.
That is often used in 'command-line single user mode' if at all; or via a
third party interface utility (onyx, cocktail, etc.)
There is no way for you to enable 'root user' at the present?
How to enable the root user on your Mac or change your root password - Apple Support
{A fair utility that runs in demo, to extract software from installer DVD/CD
that may work if you have a disc to attempt, would be [ CharlesSoft Pacifist ]
The maker site still offers at more than one version. An older ^ one is advised.}
An early version of OnyX or Cocktail was able to use hidden utilities in older OS X.
My older Macs still have copies of these interface utilities; but they usually use an
existing underlying base OS X (terminal, etc) w/ easier interface than command-line.
Not sure what to suggest ~ I'm too busy (away from computer) use to consider.
For older Mac with hard to get systems, it's always a good idea to have a working
full system clone and also the original Install-restore DVD or CD media; plus copies.