Composite or Component?
Composite is the older Standard Definition Video + L/R Audio (since you mention hooking it to an HDTV and getting a good picture, I question if this is what you are doing) Yellow + Red/White
Component is capable of supporting High Definition using 3 Video (Y, Pb/Cb, Pr/Cr) + L/R Audio and is an analog alternative to using HDMI. Red/Blue/Green + Red/White
Component requires 5 cables -- not 3 - as the audio needs to be brought over seperately from the video.
Can you confirm which you are doing and provide the type of STB and TV (models) and which connectors on each you are using (by label name of the connection).