I'm not sure, but according to what I know:
Parce que introduces a cause, explanation, or motive - it explains why something is done.
Je ne suis pas venue parce que je suis malade
Comme highlights the link between a consequence and its result. It usually begins a sentence
Comme je suis malade, je ne suis pas venue
Puisque gives an obvious explanation or justification, rather than a cause.
Tu peux partir puisque tu es malade
should not begin a sentence, and is mainly used in formal and written French.
Car supports a judgment or indicates a reason
La reunion fut annulée car le président est malade