2005 chevy equinox light rollover,no start,no security,no radio,no interior lights. turn key to on, cross at starter,starts and runs for 4 seconds.

it's a manual means my transmission is manual transmission?
with a left foot clutch ,the clutch switch is bad above the pedal clutch
that switch enables the starter relay just like all cars, manual
so you an not start engine in gear.

those other problems are other causes.
IMMO key must not be ignored. padlock
thee users guide tells you what the lamp does. (lost that?)
lost the second ignition key? from when car was new.
some cars dim HL lamps to have extra power to crank the engine, a super good features on all cars with it.
you just buy a dead car, or did it just fail out of the blue.??????????
learn what RAP is in the manual.?
key off radio works for delay10mn them or ends door open
page 2-18 in the manual

now IMMO words same manual free, to all chev. owners.
Page 2-15 actual
to start the engine closes door or IMMO Passlock
will fail.
Your vehicle is equipped with the Passlock®
theft-deterrent system.
Passlock®
is a passive theft-deterrent system. Passlock®
enables fuel if the ignition lock cylinder is turned with
a valid key. If a correct key is not used or the ignition
lock cylinder is tampered with, fuel is disabled
During normal operation, the security light will go off
approximately three seconds after the key is turned to
RUN following an engine start.
If the engine stalls and the security light flashes, wait
until the light stops flashing before trying to restart
the engine. Remember to release the key from START
as soon as the engine starts.
If the engine is running and the security light comes on,
you will be able to restart the engine if you turn the
engine off. However, your Passlock®system is not working properly and must be serviced by yourdealer.

READ
https://www.manualowl.com/am/Chevrolet/2005-Cobalt/Manual/388


but the clutch switch is failing and can be jumpered easy, your paper clip. some switches have adjustment or are just fell loose.

Check the crank/start fuse. Also check to see if the security light is on. Reset is 10 minutes on, 30 seconds off, then start. relearn is 3 times this, start after the third time, for security. If still no start, check the wire going from the ignition switch to the starter.

I am guessing that it may be the neutral safety switch

Is the security light on? If it is you may have to go though a security reset to get it to start again many scanners tell you that the system is tripped and thats why it won't start. Check first to see if the starter and battery connections are good. Take a test light connecte it the the big wire post on the starter, The starter can be seen as you lay on the ground in front of the car and look at the front bottm of the engine. The biggest wire is the battery cable there's other wires under the same nut and they run the reswt of the car, then theres a second smaller wire that comes powered when you turn the key power goes from the key to the nueral park switch, ( reset the car in park or nuetral and try again) them to the starter relay ( in the under hood fuse relay panel, ( it's maked on the indide of the lid) The security computer turns on the ground to this relay to let the car start if all the coditions are met. and them from there to the starter. energise this small bolt on the starter next to the battery cable ( cross power from the bolt to it, It may spark)(sheild eyes) and it should crank it it doesn't the starter can be bad if the battery is up good. or the cables are too dirty as the number one reason for a no start. If it does crank go back and turn the key on and see if it starts and runs crossing the starter if it starts and then dies and you try it again and it does the sane thing the security system is likly to be hiolding you back. If you have the right key. You turn the key on in the run position till the security light goes out, ( 16 minutes or so ) when it goes out turn the key off and then back on and the light will be back on. wait again with the key on for another 15minutes or till the light goes out. The thrird time you do this and the light goes out turn off the key then turn it right back on and try to start the car. It should start and the light should stay out. When your doing all this waiting with the key on turn off anything that may run the battery down radio heater interior lights and if you have been fooling around with it very long before you got to this point you may need to get the battery charged up just to make it though all of this.. A bad battery is the most likly normal reason for your car to do this and hot weather hurts batteries just like cold weather does so it's possible you need a reset and anew battery. Sure it lights the lights and plays the radio but it won't start the motor.

Vehicle not all the way in Park or Neutral? Bad battery? Bad battery cable? Bad Transmission range selelector switch? Bad Starter? Bad starter relay? Onboard security system disabling start circuit? Locked-up engine?

What is working and what is not? Headlamps? Interior dome lamps? Radio? Warning lamps on dash? Is the "Security" light flashing?

Is it making any noises when you turn the key?

will the starter do anything? click, chatter,etc., try turning on the headlamps and turn the key as if to start vehicle.,see if the headlights dim,then if so you have a good starting connection, then more than likely the battery needs a chg, radios and lights will light seemingly o.k. but a starter needs higher current to operate and this is where it will fool you, the only other thing might be is if you left the key on too long and the alarm sensed this and cut the starter power so as not to be stolen, just an idea

TURN THE IGNITION KEY TO RUN WITH THE ENGINE OFF.FULLY PRESS AND RELEASE THE ACCELERATOR PEDAL THREE TIMES WITH IN FIVE SECONDS.YOU HAVE TO DO THIS MORE THAN ONE TIME.ITS NOT GOING TO RESET FIRST TRY BUT DO THIS PROCEDURE.UNTIL THE CHANGE ENGINE OIL LIGHT WILL FLASH WHILE THE SYSTEM IS RESETTING.TURN THE KEY TO OFF.WAIT A FEW SECONDS.START CAR UP TO SEE IF CHANGE OIL LIGHT COME BACK ON.IF YES YOU HAVE TO TRY THE RESET PROCEDURE AGAIN.

Add Duplicate Key (PK3 or PK3+ key)
1. Insert an existing key into the ignition cylinder.
2. Turn the ignition cylinder to ON (RUN) and back to OFF.
3. Remove the existing key and, within fifteen seconds, insert the new key
and turn it to ON (RUN).
4. The security light will light up for two seconds to indicate success in programming
the key into the vehicle.
Originate New Master Key (PK3 or PK3+ key)

1. Insert new key into ignition cylinder and turn it to the ON (RUN) position.
The security light on the dash will illuminate and stay on for ten minutes.
2. When the security light goes out, you have one minute to start the next
step. Turn the ignition cylinder to OFF and then back to the ON (RUN)
position. The security light on the dash will illuminate and stay on for ten
more minutes.
3. When the security light goes out, you have one minute to start the next
step. Turn the ignition cylinder to OFF and then back on the ON (RUN)
position. The security light on the dash will illuminate and stay on for ten
more minutes.
4. After the security light has gone off the third time, the key has been programmed
into the vehicle’s computer and will operate the car. It has replaced ALL the
previous electronic key codes and is the ONLY key programmed into the
vehicle’s computer.

Add Duplicate Key (PK3 or PK3+ key)

1. Insert an existing key into the ignition cylinder.
2. Turn the ignition cylinder to ON (RUN) and back to OFF.
3. Remove the existing key and, within fifteen seconds, insert the new key
and turn it to ON (RUN).
4. The security light will light up for two seconds to indicate success in programming
the key into the vehicle.

Hi to reset the oil life monitor
turn the key on engine off
push the gas pedal to the floor 3 TIMES WITH IN 5 SECONDS
the light will flash then go out

I believe that yor key has a chip installed in it. your BCM will have to be programmed by the dealer.