I have a 98 Bonneville SSEi. Have check starter, battery less than a year old, battery cables have been cleaned of corrosion, alternator replaced 6 months ago. Car will not start! Have jumped off the starter and it started and then died. Is there a way to check the neutral safety switch? If so which sides should be getting power?

Usually you throw it in neutral and try starting it with your foot on the brake. If it starts the switch is either out of adjustment or bad.

1st tell us what the security light does when the key is turned to the run position. Vats (Vehicle Anti-Thief System) problems are more common than park/neutral switch.

security light just blinks constant until you take the key out and shut the door then it goes off.

Security light should just come on for a few seconds. You can try another key &/or cleaning the contacts inside the lock cylinder. Most likely you'll need to do the Vats bypass or replace the lock cylinder. Here'* a link to an article on the bypass.
http://www.asttraining.com/Files/vats1.pdf