My own opinion would be that a colon probably fits best, as both can be independent sentences and the second sentence clearly adds information to the first. So, "She was sick: That's why she wasn't able to come." The colon makes a hard pause; harder than a semicolon, but less hard than a full stop.Originally Posted by joenuts
You may then find yourself in an argument about whether the first word should be capitalized or not. I do capitalize, mainly for pragmatic reasons, because many style guides (notably Chicago) say that you ought to do so if the clause after the colon forms a complete sentence; and so many editors expect it. On the other hand, others will argue that a colon is not a sentence break, and so a capital should not be used. That is how I was taught English myself as a child. It's all rather silly, and boils down to individual stylistic preference really.
As to your alternatives, I feel the comma is too soft and so is incorrect. A semicolon is better, but does not properly convey the causal relationship. Using a conjunction would be an acceptable (and safer) alternative. It often is if you are unsure about the exact nuances of punctuation.