Semi-colons should be used where the two sentences could stand alone, but are connected.
(This would probably explain why I often use a capital on the beginning of the secondary clause. I examine the sentence to ensure it is able to stand alone, thus making it essentially a complete sentence in my mind, and thus in need of capitalization.)

Colons should, I believe, be used where the sentences are connected, but they are not complete entities.

John had an interesting way of dealing with visitors; he would answer the door in the nude.

This method had just two major drawbacks: cold weather and hysterical ladies.

Semi-colons are also the one to be used for lists.