The turn signal indicator staying on suggests a bad ground on one of the turn signal lights. MOST LIKELY the front Turn Signal light (bout other options are possible) And I stress the word "SUGGESTS".
Why?
The parking light and turn signal lamps are usually dual element lamps with a common Ground. IF the ground is bad for any reason (IE bulb not making good electrical contact with socket) power to the Parking element back feeds the turn signal circuit
WHy front
The rear turn signals are connected together as STOP lamps on most vehicles unless you are signaling a turn but the FRONT connect directly to the indicator.