Buick PA randomly won't start

1999 Buick Park Avenue
100K miles
Driven daily
Recently began not starting at random times. It's done that first thing in the morning, middle of the afternoon, after having been driven all day, etc. The car will light up as if it is going to start, we hear one click, and then nothing. Lights stay on but the car won't start.

Ideas? Help?
(We recently moved to a new area and haven't found a mechanic that we trust yet.)

You need to check grounds and battery connections first.

What is security light status when in "No start"?

What is security light status when in "No start"?
If it were a security issue wouldn't it crank during the no start?

Resistor in key systems usually don't crank when security light is on- means system is reading resistor pellet wrong- have to wait ten minutes and try again. I usually recommend trying back-up key when this happens, or vigorously wiping down both sides of resistor pellet on your pants. This happened to me in Cinci airport parking garage at midnight- the "key" was to notice security light was on- so I kept wiping down the pellet- and it worked on third try and 20 minutes later....

I agree, if light goes off after 4 seconds of ignition, then there is a connection issue- and recommend someone hold ignition switch in start position, while someone else wiggles both battery connections- if it starts, then you just figured out your connections are loose or corroded. Since you are hearing clicks, I would lean this way.....