While the old Mac still runs is the operative phrase, since Entourage's dead status means doing this now on the working machine beats any future archaeology. The routes, easiest first:

The direct print to PDF, per email: Entourage on Mac OS can print, and the Mac's print dialog has always offered Save as PDF in the PDF dropdown, so File, Print, Save as PDF saves individual emails as PDFs using the OS PDF engine, exactly as modern Apple Mail does. For a manageable number of important emails, this native route on the still running Mac is the simplest, no conversion tools involved.

The bulk problem, since per email does not scale: Entourage stores everything in a single database file, the Entourage database in the Microsoft User Data folder and bulk PDF conversion of a whole mailbox is not something Entourage itself does. The scalable path is to first get the mail into a modern accessible format, then bulk convert from there.

The export then convert route for volume: Entourage can export to MBOX or its mail can be moved to Apple Mail or another client on the old machine while it runs and from a modern client the bulk email to PDF routes this forum covers, Automator on Mac or a converter, handle the volume. The key is using the still functioning old Mac to migrate the mail off Entourage into something current, since once that machine is gone, the Entourage database becomes a genuinely difficult format to open at all.

The priority given the dead software: even if PDF is the eventual goal, the urgent action while the Mac runs is getting the mail out of Entourage into a portable format, MBOX or a modern client's storage, because that is the step that becomes hard or impossible later. PDF conversion can happen anytime once the mail is in a live format, so preserve the mail into portability first, PDF second, using the working machine for the part that only the working machine can do.