You may want to change your title to "Need help connecting N64 to Beovison 3". Especially as it is an older TV.
You don’t say if it a Beovision 3-28 or 3-32. They may have different connections/inputs and this will assist people trying to help. It will also assist to know what you have already got cnnected to the TV and what buttons are on your remote. Is it a Beolink 1000 remote or Beo4? We need to know what buttons to assist in the connection menu. In the top 9 buttons the Beo4 may say SAT, V.TAPE & A.TAPE or DTV, V.MEM & A.MEM.
As you say there may be various problems, but as it works using the front connections It should work from a SCART. You do need to “assign”
B&O TV inputs work differently to most TVs. You have to choose an input and assign a button on the Beo4/ BL 1000. The inputs are also setup for different components to be connected. On most older B&O TVs the SCART marked V.Tape is for a B&O Video recorder (or HDD1/DVD1). So plugging your adapter in there may not work.
There may be a SCART marked AV. This input may be your best bet. There may also be one marked Decoder (Depending on TV Model). But it is worth trying all inputs
When connected you need to go into the onscreen MENU and go to the connections MENU. The connections may already have something assigned or say NONE. Go to the AV input. and scroll down to find either SAT or V.TAPE. and save. Now when you press SAT or V.TAPE (depending on what you chose) on your BEO4 it should open the input. Do the same for each input you try.
Finally, if that does not work, Itmay be the XBOX adaper that is fulty.
Good luck
Stoobie