You are right, if composite and SCART works on your other TV then it SHOULD work on the Samsung.
Do other inputs (DVD players, VCRs, etc) work on the Samsungs SCART/Composite ports?
Is the Amiga running in 50 or 60Hz? I believe the Samsung should work on both but its worth a check. Try holding both mouse buttons down when powering on the Amiga, see if you can see the boot menu and if not press TAB and see if that makes any difference. (I think that's it, I am a bit Amiga rusty to be honest)
Obviously it wont work on Workbench when its setup for VGA but I assume you were already aware of that - as it wouldn't work on your other TV in that mode either.
I'm sorry I cannot be more help. Hopefully someone else had experienced and fixed this problem.