Car keeps beeping even though key is out of the ignition on a 1997 Saturn 5 speed.

There is a key in sensor, as well as a headlamp-on sensor that both can trigger the warning beep tied to DOOR AJAR. You can disconnect both systems one at a time to find out which oine is causing the warning.

Some check light on dahsboard or "theft" system there?

13 years old, time for a new clutch.

are your lights or fog light switch on ??,

It sounds to me like the ignition switch is going bad. Don't know how hard it is to replace one But if you go here you can look at one
http://www2.partstrain.com/store/details/Saturn/SL1/AC_Delco/Ignition_Switch/1997/Base/4_Cyl_1-dot-9L/ACD1435D.html?vdesc=true
Hope this helps
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i have a 1997 honda accord and i need the radio code for it. my serial number is M96G146085

ignition switch broke or the car is dieseling the idle speed is too high throttle valve stuck open or the valves and heads full of carbon build up.causing preignition.

the shift interlock fuse may be blown. check your fuse panel.

If you are using the smart key and you do not have it in the ignition, it will send a signal thru the car speakers to let you know that the keys are not in the ignition(beep,beep,beep,beep), and that they are to far from the sensor. Next time you are driving and the keys are in your pocket, pull them out and wave them around the speedometer. It will notice keys in car and the beeping will go away.