My 90 buick riviera is having cranking issues?

[Kevin B]

My riviera won't crank. When I turn the key nothing happens but i do hear a click come from under the dash and the dash board lights and radio come on. The battery is new and the cables are tight and clean. The security light do come on when trying to start the car. I havent got the car to start since yersterday. The only way to get it started is keeping trying every 4 minutes for like 2 hours then all the sudden the car will start but if ou cut it off you got to go through the whole process again. This same problem happen to me a year and half ago and i had to replace ignition switch and lock cylinder and starter. Any ideas what could be the problem. Im thinking its the lock clinder agaim not reading the key. I have a1990 buick riviera 3.8 v6