Übersetzung - Deutsch-Englisch - Aristophanes konnte in der Vertretern der...

Well, I thought "eingebildeter" was a genitive related to "Macht", such as "vergangener", so it should be something like :amusing characters of a conceited but basically long gone power.
By the way, I forgot a "de" in the first "eingebildeter", but wrote it right in the message.

Yes, you are right, "eingebildeter" refers to "Macht", which means "power" and not "world", by the way. I was worried for a few minutes until I found out where the "stuck" comes from. "Im Grunde" is a kinda set phrase for "basically, after all, in reality", i think that made the difficulty of the last part of the sentence.
Concerning the comment for the German source text: the French word "cultivé" means "gebildet", "eingebildet" is unfortunately something very different: it can mean both "imaginary, fictitious" and "conceited, vain".
Hope I could help, sorry I didn't see your message before now.
Greetings

Okay, I'm back. I saw Apple's request to me for more comment. (Why don't I see my original comments? I am trying to remember what my original translation said...) A couple of points. I read "eingebilter" as a typo for "eingebildeter", no problem there. The problem I see in the original German (at least what was posted here) is the lack of a verb.

Eingebildeter is stuck up, conceited, etc. I think the French "cultivé" is an error.

Yes, you can parse "eingebil[de]ter, im Grunde laengst vergangener Macht" as a phrase, in which case it is "conceited, essentially long gone power" but then you are left with "amusing types, conceited ..." which is not grammatical nor does it make sense to me.

I confess to some improvisation in my translation.

Silk from a pigs ear, anyone?