Forgetting about digital connections such as HDMI and DVI, basically there are a number of ways to connect a STB to a TV via scart. Composite, s-video, RGB and for a few TVs: Component. Most likely does you BV3 only accept the first 3. You will not be happy with the picture quality of composite or s-video. The converter you tried did composite or s-video, depending on the which connections you used.
This leaves you with two potential solutions: Some STBs will be able to send out RGB via the component outputs (the Red, Green Blue RCA outputs) This would most likely be a menu option somewhere on the STB if available. Next challange will be to get a cable with Component in and Scart out, as most cables are the other way around to support STB with Scart for a Plasma without.
Other option is to get a component to RGB converter. Have not tried any of them, but it could easily set you back USD100.