90 Buick Lesabre - Starting problems

I have a 90 Buick Lesabre that has been sluggish starting. I thought it was a weak battery, so I had it tested at two separate locations and the battery is still showing a full charge and good. I then checked my cables and they are good and tight with no corrision. The alternator is less than 1 year old. It now is at the point where the igintion will not even click. I also tried to jump start the car thinking I may have a bad battery cable; however it would not turn over. Could this be a bad starter or the selenoid on the starter? How can I rule out the starter from the selenoid?
Any suggestions would be helpful.

A replacement starter comes with a solenoid. Just replace the unit. It sounds like both may be shot. A sluggish starter pulls high amperage and puts a burden on the solenoid during starting. Also, be sure your cables are in good shape.