How do I reset the security system

Resetting the Passlock system should fix it. If it doesn't you need an auto electrician or an auto locksmith.

https://www.google.com/search?q=2001+gmc+yukon+security+system+reset

..

This may be related to the antitheft system The system is known for turning off the starter and/or injectors when it fails. Is there a light on the dash that says SECURITY? This is a common problem worth looking into. http://www.diy-gm-security.com/

security system or theft deterant system how ever u want to call it
install battery and if u have key remotes hit lock and unlock this should reset system if no remotes insert key and cycle from off to on (do not start) three times and then try to start

The security system thinks that something is wrong and is sounding the horn and flashing the lights. This is because the system had no battery power. Unlock all the doors, put key in ignition turn all way except to start the engine. remove key from ignition and lock all doors, This may reset the security system.

It happens a lot for the Tiburon apparently....what you have to do is put the key in the ignition whilst the horn is going nuts, turn the key to the "on" position and wait a minute or so for the horn to stop blowing. Then press the "unlock" button on the fob until you see the turn signals flash. try turning the key over and see if it will start up. If it doesn't, try again, same thing only turn the key all the way off and try starting as normal again. I can't remember if it's the "unlock" or "lock" button you're supposed to press, but one of them does it. Test it while in the car and see if it locks when you hit lock on the fob.....oh, and also make sure all the doors are shut while you are doing this. It recalibrates the fob to the car's computer and resets your security system and keyless entry.

You do have a security system. This should be transponder type security system, I don't believe it will start without key fob. There is an inhibitor relay for your starter motor circuit and security system. Check for applicable trouble codes, if there are any? Maybe you local dealership, talk to service department, see if they can get you a key fob. Go at it that way. I don't know about the cost?
You can usually jump the starter motor to see if it will crank the engine, but, that doesn't mean it will start. If you try that, make sure tranny is in park or neutral and parking brake is set. Safety is your responsibility.

If it is a factory (OEM)security system. Go to passenger door and lock/unlock 2 times to clear/reset fact security system.