If the composite picture is no good and you are sure your cabling quality is ok, then it might just be the screen you have bought. The picture from my pi to old crt via composite is usable.

Have you tried the composite output with any device, or tried the new screen with another device ?

Your question is lacking detail though – you mention nothing regarding cabling, which exact options you have tried etc – so it might be an idea to be more verbose so people can advise and point you in the right direction (and if that direction is a website with a solution, then so be it)