A few comments…
The BL14 system is an active (means that the ampflication is built in) loudspeaker set.
It is meant to be used with an audio device that has pre-outs or the normal speaker outputs.
That is what the adapter is meant for.
You should be able to get this still – maybe on the used market (?).
The RJ45-Powerlink connections are for connecting to a Beovision as the source (which is a tv with audio processing and pre-outs built in).
P.S.
My best advice would be to contact Steve@SoundsHeavenly for further advice.
You can find a link at the bottom of this site (he is a sponsor of Beoworld).
P.P.S
You can find more about the BL14 on the old forum – e.g. here:
https://archivedforum2.beoworld.org/search/SearchResults.aspx?q=Beolab+14&o=Relevance
MM