ところで、[sentence]
ところで at the start of a sentence means "by the way": it drops the current topic and opens a new one. It works in casual and polite speech alike.
It comes after one topic has been wrapped up. Dropped into the middle of a related discussion, it sounds abrupt.
The two look alike but do different jobs. ところで changes the subject. ところが stays on it and says the result was not what you expected: "but then".
ところで carries no contrast, so it never stands in for でも or しかし.
After a た-form verb, ところで is a different pattern: たところで, "even if you did, it would be no use". It sits inside the sentence rather than at its start.