My 1999 Blazer keep stalling, and now won't start, what should I do?

I WOULD CHECK THE FUEL PRESSURE, OR EVEN SMACK ON THE BOTTOM OF THE FUEL TANK , THEN SEE IF IT STARTS , IF IT DOES THEN YOU WILL NEED TO REPLACE THE FUEL PUMP, FUEL PRESSURE IS CRITICAL ON THIS APPLICATION

along with what white154 said make sure your keys dont have to be chipped with the security system if it does take it to the dealer have new keys made or have the security system reset

If the security light is blinking, then yes its a "passlock" problem. Try this: http://old.kingbain.com/how-to/how-to-permanently-disable-gm-passlock-system.html