You will need the base station of the beocom 4(not beoline) (wich has the charger build in it) and allows the beocom 4 to make telephone calls.

I guess you can buy it as a spare (they probably aren't linked to a specific beocom4)

I do have the base station. There is one cable going to the base station. At the end of the cable there is some thing like a "splitter" connected which has two input jacks: one for power and one for line. But I don't have any device looking similar to the power adapter that is shown in the instruction manual. And I was also not able to use it without this splitter connecting it directly to the (analogue) port of my WLAN router with VoIP function.

What am I doing wrong?

you should check the manual on bangolufsen.com

The power adaptor is required to both charge the handset and power the base station.  Without it you will not get it to work at all.

Opman

No the charger is not built into the base, it is a separate adapter. Of course it is needed for the phone to work, other wise you can not recharge the battery. You should be able to source one from your dealer.

Allright, I will try that. Thought it would be possible to use it without a power adapter since there are some phones that use electricity straight from the phone line. But it seems like thats not the case for BeoCom 4.

you absolutely need the power adapter!

i replaced a damaged one some time ago, ordered right from the dealer, i don't think it was more than 40USD.

The power you can use from the telephone line is very limited when the line is unused. The power is nowhere near enough to drive the radio part making Beocom 4 wireless. The power you can use is not even high enough to drive the display on the corded telephones like Beocom 2500 etc. which is the reason for the batteries in corded phones with display. 

When the phone is ringing you can use a lot of power and when the phone line is busy you can use approx. 1/6W. This is enough to drive the radio, but then your would only be able to use the telephone to accept a call... you would never be able to make a call.

Anyway, as written by others you need the power adaptor which supplies both the electronics in the base station aswell as the charging stand integrated in the base station. You could try to make contact to the seller and claim that the power adaptor is a part of the telephone and that the seller should send it to you.

Br,
Burnix