Car does not start

The car start when tripped from the start, but goes off after few seconds, if I try to started with the key it wound make any noise at all.

I already check all that and were found okay.

My 1998 chevy lunina car sputtered and stopped just short of my driveway. I tried to restart but everytime I went to turn into the driveway it stopped again. My husband went out the next morning to try to restart it It almost did then cut out. He tried it again and there was nothing. So he put in a new starter, battery fuel relay switch, map ssensor and still nothing. The starter gets hot when he attempted to start it twice what is happening?

When key is on all idiot lights are on my radio plays the dome lt is lit the headllights are bright and the horn works

Where is the starter relay located?

I put in 2 used starters--both seemingly bad and 2 new ones (i had taken one back and had it checked and it was definitely bad--had this last one checked before I took it home and it tested good) checked fuses all good thought of the ignition switch which is located in the column right? But my husband is reluctant to try that. Not sure where transmission position switch is located. Thought also of the ignition coils No one seems to know why the starter gets hot after trying to start it once or twice.
Everything happened so suddenly--no warning noise

When we try to startup our Lumina. The engine doesn't crank at all. The dash lights come on but nothing happens when we turn the key.
First time I thought the car might have been out of gear so I moved the shift to N. Then back to park and the car started up.
This happen intermittanly for a month.
Each time I could get it started by doing the above method. Sometimes but not always.
Sometimes it would just start by trying for a couple of minutes.
That was last summer. 10 months past and it never happens again. Forgot about it until the other day.
My wife tries to go to work and she can't get it started. Calls me. I try first time and it starts up.
Happens again. This time I can't get it started.
Go get my keys, try it and it starts up.
Any ideas will be appreciated.
Thanks

Thanks for the quick reply.

When you mentioned security system, I broke out the owners manuel. The cars comes equipped with a security key. If it is damaged or the wrong key, it will shut down the starter and fuel systems for about 3 minutes. That's why it started when I switched keys.
I believe that's the problem.

Thanks for your help.

Engine Performance problem
1998 Chevy Lumina

I love my little Lumina. Back last fall I started having problems with it. It would run fine to work, when I'd leave at the end of the day it wouldn't start. Once it's jumped it would run just fine for a couple of weeks. Then it started happening more often. It's been to the garage several times. They put in a new battery. Tested a few other things, everything checks out good. The last time for about 10 days, they took the car to another garage that has GM software and hooked the car to that. They can't find anything wrong. Now it's happening almost every day. There are lights, radio, windsheild wipers, everything, it just won't start. So I have 2 garages of mechinics that can't find the problem, anyone have any ideas?

Thanks

Thanks for the help, but there is no security system on the car.

Will not crank. Replaced battery, replaced starter.
Lights work, locks work. When you turn key. Nothing; no juice to starter; but current is working throughout car. HELP!

I have a 1998 Chevy Lumina, it has been extremely cold here, -20 degrees I went to start the car in the morning. It turned over slow but started I went inside to let in warm up. When I came back out the car had quit. It would not fire again, so I let it sit. The next morning the exact same thing, everyday since I try it turns but will not fire up. What do you suggest I do?