Either the idle is set too low or there is mostlikely a fuel issue... You could have a bad fuel filter or fuel pump.l
Most likely a Throttle position sensor
Next time it won't start spray a little starting fluid into the air cleaner then immediately try to start it. If you don't get a response you probably don't have any spark. If you get a response even briefly you have a fuel delivery problem.
try checking the IAC motor. if it stalls at idle then it could be that. or the egr valve. one of the two have to be contributing to the problem
I have a 93 Corsica and had this problem. 1. crank sensor 2 ignition modual 3. main brain. Ck codes at a shop. Some will do this for free.
check your idle controle moter. it is probably crudded up or not wotking.
Check the EGR valve.
Could be a vacuum hose disconnected. Most likely the half inch diameter one attached directly to the intake manifold, if engine won't even start.
Start with replacing the fuel filter.
first is the air on you may need to thoroughly clean the air mixture assembly where the breather tube connects the engine
check all vaccum lines since it is an 84 i would replace all lines
I may be wrong but it sounds like your alarm is the problem. This happened to my brother's van(Astro). The built-in cutoff switch in his alarm was preventing the van from starting. It may be possible to disconnect the alarm system and try to start it. That's what my brother did and it worked.
Determine the problem and see if you can fix it or not. If you cannot determine what's wrong then find someone that can. A trick to starting a vehicle is to pump the gas while you turn the key in the ignition. There are a million different reasons as to why a truck won't start.