Is lack of your own tie fighter's engine noise normal in the '94 version or do I have a technical problem?

Totally normal. IMO it was a poorly done afterthought in the '98 version to distract from the redbook music…

Does anybody know a way to remove the sound? X-Wing has an option to turn it off, but it seems that the Tie Fighter does not. That sound is really annoying. Is there, for example, a effect file I can remove? Or something?

EDIT: And of course I mean the sound from the Windows version of the game as the DOS version does not have this annoying sound.

where? dat friggin loud A-Wing is killing me! you're not talking about deactivating sound effects completely, are you?
cause you can do that also in tie fighter. and i wanna hear ma lasers and explosion and stuff.