As RapidRobert wrote, it's not the fusible link, because you have power, otherwise you wouldn't have any lights, etc. It would be like there was no battery in the car.

MarkM gave some good advice on the ignition switch. Run your hand down the left side of the column and find the ignition switch and see if it's loose. You'll have to remove the plastic cover that uses plastic press ins to fasten. See if the switch moves up and down, even a little. If it does, try moving it while turning the key to start car.