I started out as a fair weather commuter. After a while, I started taking more and more chances that it might not rain, because I enjoyed riding more than driving. After a while, I just rode anyway and found out I didn't melt and changing out of wet clothes didn't matter much at work. I have a nice place to dry my clothes in front of a fan though.
After a while I challenged myself to see if I could go a whole year without driving to work. My end goal was to sell my truck and go down to a one vehicle family. We did that last spring. It's been almost a year since I decided to sell my truck.
As for when I feel sick, if I'm too sick to ride I shouldn't be at work. Although I find that my illnesses are much less severe than when I wasn't biking every day. If I don't get enough sleep, I do better riding than driving. I feel more alert for most of the morning.
If you really want to ride instead of drive but lack the motivation in the morning, just make it harder to drive. Give your keys to a neighbor, freeze them in a block of ice, or make sure your car tires are so low you couldn't possibly drive without pumping them up. Anything that would make it inconvenient to drive.