Battery went dead on my 2000 Bonneville so I had.

Yes, I did try the relearn process without success.

I unlocked the car using the key in the drivers door and hooked up the
battery charger so the battery wouldn't go dead during the relearn
attempt. I turned the key to the on position and waited over ten minutes
and the security light never went out. After eleven minutes I turned the
key to the off position for approximately 6 seconds and then turned the
key back to the on position and waited again for eleven minutes. Repeated
the process a total of 3 times and the security light never went out and the
car still wouldn't do anything after the completion of the relearn attempt.

On another attempt at the relearn procedure I waited for over 15 minutes for
the security light to go out, which it never did.

There are no codes showing in the code reader. The service engine soon
light is on as is the security light.

I took the master key off of the key ring when performing the relearn procedure
so there was no other interference during the attempt.

Any other ideas?

I have an OBD II code reader.

I hear the fuel pump whenever I turn the key on.

Before I replaced the battery I jump started the car and it ran okay.
When it wouldn't restart I took the battery to Autozone and they
tested it an found it to be bad. Hence, a new battery was installed.

The car does have a GM keyless entry remote which I removed from the master
key when I did the relearn procedure.

Yes, the remote locks and unlocks the doors.