Why does the security light flash even when key is on and engine will not start?

The security light flashing is the indicator. The fuel pump is disabled by the ECU because the immobilizer system does not recognize the transponder chip inside the key.

There could be several causes.
a. Either the transponder chip inside the key is bad, not programmed, or missing
b. The antennae that is located around the ignition lock is bad and/or not reading the transponder chip inside the key.
c. There is a wiring issue between the ECU and antennae.
d. The ECU is bad

You may want to seek out a qualified mechanic or automotive locksmith for help, not all mechanics and/or locksmiths are capable of handling the immobilizer systems on these vehicles. So be clear when discussing your problem to them and make sure they are capable of handling this type of problem.

If the key is not original, check to see if it is a cloned key. Some cloned keys use batteries, when the battery inside the key dies, it no longer communicates with the vehicle. Although it's not common, regular transponder chips can go bad, usually due to physical damage.

An immobilizer transceiver coil tester can be used to test the signal from the antennae at the lock cylinder.

If the ECU is determined to be bad, a used ECU with matching part numbers can be used as a replacement. Contrary to what a dealership or some shops may tell you, all that is required is an immobilizer reset service on the used, replacement, ECU to get it to function with your vehicle. A used ECU and an Immobilizer Reset Service is much cheaper than a new ECU from the dealer. Make absolutely sure that this is the problem before going this route though.