I want to add a remote start, what passkey is on 2003 astro?

Disconnect Astro battery and battery in remote. Leave that way 10 minutes, reconnect Astro first.

Its possible the remote code was changed after install which required a learn and the learn was erased when battery power was lost.

If this is an add-on aftermarket alarm system, the best hope is that somewhere under the dashboard or near the left kickpanel by the floor you see/find a small button mounted there. This is usually the most common install for the override switch by most alarm installers. Turning the key to the ON position then pressing the button and holding for 2-5 seconds will shut the alarm down in most cases if it has such a button.
If it does not have a button, or this is a factory alarm system, its possible the alarm control module fuse has blown or the module itself is stuck or failed, or the receiver for the remote is not seeing the remote. Recheck the connections at the battery, if its an add-on alarm there may have been a constant power loop attatched to the cable that is required to power the receiver/module and was accidentally left off. checking all fuses may also yield a blown fuse that feeds the alarm system controls.

driver side system

If you don't have the remote then its pretty much useless. I have seen at Pep Boys where they sell replacements for the factory/dealer installed alarms. Or just remove the alarm completely and reconnect everything the way it was.
Without knowing what brand alarm it is a person cannot honestly answer how to disarm it as they all work differently.
If you know a brand and model you may be able to find downloadable instruction on the manufactures web site.

I know this sounds obvious, but did you run your battery dead? If you don't know, get the battery checked.as for as tuning off the alarm... Just simply disconnect your negative battery cable. This will reset the alarm. This doesn't solve the problem but makes it less annoying while figuring it out. What about the battery in your remote, is it dead? Look for any wires from the alarm that may be frayed, cut, or corroded. Hope this helps.

If the passkey is messed up, there will be a light on the dash that says security, or have a picture of a car with a lock thru it. If there is no light when the key is turned forward, then its NOT a passkey problem.

You need to find the remote. Once you do,you can use it to turn off the alarm by pressing the unlock button. You can also try pressing the unlock button on the door panel but, I don't know if that will work. You might have to have another remote programed for the vehicle. You can also try putting the key in the door lock and unlocking it.

leave the key in the ignition, turned to 'run' (just before the crank position) and leave it there for about 15 minutes-the security light will then stop flashing-do NOT turn it off, turn it to crank and start the car. You have a security module that is not seeing the same resistance in the ignition switch as it expects, meaning you will have to either replace the ignition switch (expensive) or bypass the module (easy and inexpensive)-I have done lots of these, requires about 15 cents worth of parts and can be done in 1/2 hour.

You have interupted the passkey antitheft system. This link may help you. This is very common on GM vehicles. Do It Yourself GM Security bypass

You can't disable it, you have to buy a bypass modual to bypass it during remote start, the wires are in the ignition harness I have them in stock if you need one