No. Use a code scanner to find out why the check engine light is on. You can borrow, rent or buy a code scanner from most auto parts retailers.
Probably a stuck solenoid.
I would check the starter solenoid before I investigated the starter - it's likely the cause. Have someone try starting the car hot while you measure the voltage between the starter side of the solenoid and negative - you should get battery voltage. If not, the problem is the solenoid (or somewhere before it, electrically).
check the solenoid, and the starter.
It is the selonoid unforutnately it is built into the starter......so you probably have to purchase a new starter....about 170.00
The positive battery cable connects directly to the starter. Depending on what type of vehicle it is, the solenoid is either on the starter or on the inner fender. Power for the solenoid comes from the ignition switch. You can run a wire to the solenoid to cause the starter to engage.
Weak battery? Loose or corroded battery cables? Starter solenoid?
Dead battery, bad starter, or defective ignition switch.
That clicking sound could be the sign of a weak, if not a totally discharged battery. Or, it could indicate a defective solenoid in the starter, or a defective bendix spring in the starter. If you are convinced that the battery is not the cause, I'd focus on the starter.
Defective starter (brand new broke) Is in gear (try in neutral) Seized engine (can you turn it by hand? Does a new engine help?) Seized accessory (try removing belts) Hydraulic lock (fuid in cylinder, try removing spark plugs)
There is an electrical problem between the starter switch and the starter solenoid. The most likely cause is a loose connection at the solenoid or the fusable link has melted.
A starter solenoid can be bypassed by connecting a jumper wire between the battery and ignition posts on the starter. This will cause it to spin immediately without using the ignition switch.
The battery might be dead, or your engine might not work. *EDIT* Check your ignition coil, or starter solenoid, instead of saying "your engine might not work". If you take a hammer and tap the starter when somebody else is cranking the vehicle then you need a new starter.