The headlights should not turn on just by starting the car so your right side is working fine.
I think your issue could be easily corrected by double checking and re-seating all of the connections on the left side. Sounds like something just got plugged in backwards or has a bad connection.
Without the car on and with the hood up I hear a whine from both my ballasts too but I cant really hear it otherwise. I did not buy Hiking1978's ballasts.
Did you get the "Angel Eyes" to work?