What is connection between security light and no start Saturn. Sl1 2002?

If you jumper the fuel pump relay under the hood will it start.

Are you sure this vehicles security system wasn't breached before you bought it? Some GM vehicles and saturn is a gm vehicle. Flashes lights and gives a security light on the dash when a car was attempted to be started without the proper key or improperly jumped which sometimes burns out fuses. I hate these cars too many electronic issues.

Check if security light is on, if so, must reset. To reset, put key in ignition and turn to on position. Security light will start flashing on and off. Leave key in on position until security light stops flashing and turns off completely. This will take approximately 10 minutes. Then turn key off and take out of ignition. Put key back in and start car. Should now start

Could be starter, battery, battery cables, security key system module going bad, etc.
Check easiest things first. Battery condition and age, condition of cables, and connections at starter.

Here is a link that will help with the SECURITY light.

http://vatspasslockpasskeysecurityhelp.yolasite.com/

The gears locking up is a completely different problem. Unrelated to the security issue.

I know that when the security light comes on, it can shut down your vehicle. Here is a link to some info and ways to beats this problem

http://vatspasslockpasskeysecurityhelp.yolasite.com/

Check our this link. Explains the security light and how to fix it. http://vatspasslockpasskeysecurityhelp.yolasite.com/

If it is a problem withe the security lock you should see a little yellow key in the dashboard when you try to start. Does your key have a chip inside? Check all the connections from the battery to the starter and to the ground. Does it click when you start? If not, check the starter relay. Also check the cable connections right at the ignition.

no you might need to replace the ignition switch

lock the car using the key to reset the alarm