According to my etymological dictionary, German "Pech" is from Latin pix "pitch" (the sticky, tar-like substance) and thus related to English "pitch" -- and the meaning derivation in German may have been "pitch > hellfire > punishment > bad luck". (For the "hellfire" bit, compare also Pech und Schwefel "pitch and sulphur" which is used a bit like "fire and brimstone" in English.) Or possibly from sticky pitch used to coat branches in order to catch birds -- those birds would then Pech haben "have bad luck; literally, have pitch".
That's right as well -- that's the only word I'd use for "sin" in German.
To bring the circle back to Welsh: I've heard that in some northern dialects of German, (the local dialect equivalent of) "Sünde" is also used like "(that's a) pity" like Welsh bechod is.