Garden Update

I started my seedlings in egg crates a couple weeks ago and had them germinating on top of the fridge under a fluorescent light. They came up quick and grew well for almost a week, then they wilted and died... so sad. I put so much effort into it and I'm not terribly sure where I went wrong. Possibly, I shouldn't have started the seeds in a compost mix that I baked to sterilize it? I am going to start seedlings in pots outside in about a week. Hopefully that works, I really don't know how many set backs my optimism can take before curling up to die...