Check Coolskin here for information on what cable to use. He has a Mini connected to a BV 7-40, and it took him some time to get it connected right without the black bar on the side. Turned out it was related to the choice of cable. If I remember correctly he used a 24-pin DVI cable in the end. http://www.superwarehouse.com/Belkin_10-Foot_24-Pin_DVI-D_Video_Cable/F2E4141B10-SD/p/36451
I think you'll need a TOSLINK Optical to Coaxial S/PDIF converter to connect the digital signal to the BV7. As far as I know it doesn't accept a TOSLINK Optical signal directly; you'll still need the TOSLINK Minijack Optical to TOSLINK connector to connect to your converter -- and then a 75Ohm digital coaxial cable from the converter to one of the coax digital connectors on the TV.
However - ask here whether anyone has experience with the BV7 decoding surround information from the Mini correctly, and whether that requires a specific setup.