99 olds will not start

Non working turn signals will not drain the battery because they work when the key is on. You may have a bad battery. If your signal lights come on and do not flash, you have a bad flasher which should be located under the dash area. As for the battery, most parts houses will check the condition of the new battery for free. If you think you have a bad battery, make sure that it has a good charge then disconnect it from the system by disconnection one of the cables. If the battery goes dead overnight then it is self draining.

This may be related to the antitheft security system. The system is known for turning off the starter and/or injectors when it fails. When it's the security locked out starter, you won't even hear a click when you turn the key. Is there a light on the dash that says SECURITY or a picture of a car with a lock through it? This is a common problem worth looking into. http://www.diy-gm-security.com/

When the start for 2-3 seconds and die it's mean just one thing usully , you need to check if the security light blinking and if it doe's you need to call the locksmith to program the transponder key. Locksmith East Aurora Ny 24 Hour Locksmith 716 249 2944 in East Aurora Ny

does the DIC say "Clean Key - Wait 3 Minutes"? If so, your PASS-Key II anti theft system is starting to act up. I had the same problem in my 99 Aurora for years, until I bypassed the key resistor with a resistor pack. Google "PASS-Key II Bypass" and you should find others with the same issue. Check this link out. http://vats.likeabigdog.com/
I went to RadioShack, bought a package of different resistors for ~$10, used an ohmmeter to measure the key resistor (they differ from car to car) and then made a resistor "pack" to mimic the key resistor. Now the tricky part is that you have to take off the dash panel under the steering wheel, cut the resistor sensor wires from the ignition switch, and then solder the resistor pack in between the cut wires. Basically you're fooling the system that the key is in the ignition. It hasn't been completely fool proof (when the car is really hot in the summer, sometimes I still have the same problem - may need more temperature stable resistors), but it has been SO MUCH better than before I did the bypass.
Hope this helps, and good luck!

There may be a short causing the relay to turn the lights on and off.

check starter for power...at connections

battery is dead again let it charge longer then try it.
clean your cables and then have the alt and battery checked if they are both good then something is staying on like mine my brake lights stayed on once and killed the battery
good luck

try another key. if this doesnt work the wire in the tumbler assembly most likely broke and you will need it replaced. ( Ignition Switch)

How old is the battery? Clean the connections, charge the battery. Try starting it. Get the battery tested at Autozone or some place like that.

flicking paring lights and buzzing in steering col. is caused by the multifunction switch.(directional stick)its caused by too much grease in switch and overtime grease travels inside the connects and shorts it out.that buzzin sound you here is actualy your parking lights coming on and off so fast it sounds like buzzin.there is a solution online that u take off the steering colum cover underneath and where the little holes are on the multifunction switch you blow contact cleaner and compressed air and it seems to get or at least push the grease outa the connectors.it seems to be a good solution but problems may return after awhiles.only other solution is to replace the whole switch.
as far as the blower motor changing speeds by itself,sometimes shutting off is caused by the blower control module located under passenger dash.if theres other issues with your cars electronics i would have the body control module tested as well.thats located under the drivers side dash.
the traction control light coming on and off is more than likely related to a bad sensor on 1 of your wheel hubs.theres 1 sensor for each tire and they are know to go bad on all gm cars giving traction control issues.on aruoras they r connected to the hub as 1 unit so u have to replace the whole assembly (cant just replace sensor)