I am curious...what happened at DPS? Did their handling agent give OP any documentation / instruction?
Yes, as SilverChris said, IATA rule is that the last carrier handles any baggage related issues.
Since OP did a "domestic" AC flight -> YVR or YYZ -> TPE -> DPS, US DOT has nothing to do with this.
BR is a very structured company so just follow their process and they will get back to you. Also, see if your credit covers any of this.