You probably need to put an ADSL filter between the phone and the socket. When you have a PSTN line and ADSL coming over to your house in a common pair, they use different frequency bands (the phone is baseband as always, and ADSL is configured at the provider end so that it will only use frequencies above that). So in principle they won't bother each other, but the telephones can still "load" the upper frequencies enough to prevent the ADSL connection from working.
Your other phones may have this filter built in, or the Beocom 1000 may be more "hard" this way, being old technology. Anyway, you should be able to get the necessary filter quite cheap - it plugs in the wall socket and has separate outlets for the telephone and the broadband modem. You don't have to have the ADSL modem in the same socket, just connect the Beocom through such a filter. Hopefully it is simple as that!