ところで

ところで shifts topic with no surprise, closing one topic and opening another. ところが shifts topic because what follows contradicts what came before.

といえば takes its cue from what was just said, by association (京都きょうとといえば、紅葉こうようですね). ところで drops the old topic entirely, with no link needed at all.

ところで drops the old topic and needs nothing to link back to. じゃあ instead builds its next move straight off the last turn.

ところで cuts to a brand new topic, nothing connecting it to what came before (ところで、明日あしたの予定よていは？). そういえば instead makes the new topic sound like something you just remembered (そういえば、明日あしたは誰だれの誕生日たんじょうびだっけ？).

ところだ always follows a verb, marking where an event stands now (食たべているところだ). This ところで never follows a verb, though a verb before tempts a たところで misparse.

ところで changes the subject, and any continuation may follow. たところで needs a た-verb, never opens a sentence, and always ends in denial.

ところから explains a reason for what was just said (話はなしが二転三転にてんさんてんしているところから). ところで instead drops the old topic and opens a new one (ところで、話はなし変かわるけど).