left signal light on?

Bought a 2005 mk5 tdi Jetta used. Trying to fix all the little problem. Noticed the front drivers side turn indicator doesn't work. So I thought. Someone had just turned it so it wouldn't run down battery. It also doesn't blink. When you have it plugged in, the key fob will not blink any lights. When you unplug key fob blinks lights. Any suggestions where to start? Thanks

Anyone? Front drivers side turn signal will not turn off. Even when the key in off.

Just a guess...Might be related to the emergency flasher controller. I believe that circuit will work without the key on.