1996 Chevy Camaro

Car makes a clicking sound underneath the dashboard. Car will not start until clicking stops, it usally clicks longer when it is colder outside. When car is making clicking sound the security light and seatbelt light on dash are the lights that flicker insync with the clicking. As the clicking slows down so does the flickering of the lights. When the security and seatbelt light turn solid, clicking stops at same time and then the car will start, any information about this would be really helpful, I have been trying to figure this out for quite awhile now, I replaced the battery, because I thought it was weak, but this did not help.

Thank-you