Sounds like your headlight switch has failed. I have a 99 Audi A4, and when mine died, it was the same exact problem (it's a known problem area for the Audis). Given that your car is behaving the same way, I'd look into a new headlight switch as a solution. The toggle-for-highbeams feature is wired separate from the normal headlight wiring and is a simpler contact setup. The contacts and wiring and switching for the low and running high beams is more prone to failure. You should be able to find a switch assembly at a salvage yard for less than $15 and can probably change it yourself in a half hour to an hour.