You need a correctly wired SCART cable.
When TV's were CRT based (analog) the voltages on the wires directly drove the electronics which produced the picture. If they were slightly wrong (voltage level wise) it didn't really matter, you still got a picture.
Now LCD TV's are digital and the SCART inputs are sampled and converted to digital and then put through a video decoder to produce the picture. If the analog inputs are out of spec then the sampler and video decoders don't (always) work.
Your RGB SCART cable needs to be fully wired. It needs to have the right voltage on the CSYNC, BLANK & AVSEL pins.
You can either get a new guaranteed to be fully wired SCART cable for £17 from AmigaKit
http://amigakit.leamancomputing.com/catalog/product_info.php?products_id=226OR you can try to make your existing one compatible.
Notice all the ground connections and the values for the resistors. (Ignore the optional composite connector)
