1) a few times a week,when I turn the key in the ignition, the engine does not start- instead, I can hear the very beginning of the engine attempting to start for just a split-second(the engine never actually turns over- there is only a split second of engine [starter ed] activity- it reminds me of when a battery is all but dead and has just enough juice to make a "clicking" sound in the engine before going completely dead). All of the power comes on, but the engine does not start. I have to turn the ignition off completely, then it will always fully start with the second try. I would estimate that this happens 5-10% of the time. Local Audi dealer has looked at it, but says that they can't find anything wrong.
2) when locking the car with key fob, alarmusually chirps to confirm engagement- within last week, the chirp was much quieter for a few days- now there is no chirp at all when I lock the car. Car still locks all doors, lights stillflash,and light on door sills are flashing to confirm that alarm is engaged. Any thoughts??

thanks for any input!

I had the exact same issue with the starter on my 2004 A8L two months ago. The dealer couldn't locate the problem. They tested and thought a couple of relays were bad. After replacing, they started it fine 24 times in a row. The 25th time it acted up again. Long story short, they had my car for 12 days and the final fix took about an hour. They connected the car to the internet and had it remotely diagnosed by Audi engineers. Some sort of non-published update was needed for the controle module. There were no bulletins or articles about the problem that the dealership could find, so the last resort after nearly two weeks was to connect the car to the internet and have it worked on by someone else. The car has been fine ever since.

If your dealer can't find the problem, have them call Midwestern Auto Group (magcars.com) and ask for Marty or Josh in Audi Service. MAG will recall this problem given the fact they spent dozens of hours trying to diagnose it.