Try carefully scraping the mold off and not watering for a while. My herb kit did the same thing and now it's fine.

You really do need drainage holes in your containers, ILB.

Al

If it's not too late, I agree with tapla--add drainage holes ASAP. Sounds like you might be struggling with a commonly-known problem called damping off--sometimes, it waits until the sprouts are up, and then the region of the stem right next to the soil turns brown and shrivels and the whole thing keels over. Other times, it just inhibits the growth of the seed before it even gets to that point. Either way, it's obviously fatal to the seeds/seedlings.

All might not be lost though: if you can get some of the excess water off, there are a few techniques, all of which I have used with success, at preventing damp-off. The first is to brew yourself a nice cup of chamomile tea. Remove and save the teabag. Sweeten to taste, and enjoy. Now, take that used teabag, and make a weak tea. Dilute it to tepid temperature and use it in a spray bottle to soak the surface of the seed-starting medium. I successfully grew begonias using this method--and they're INFAMOUS for damp-off. Most can't keep the surface of the soil damp enough until the plants are big enough to water from the bottom, but spraying the surface works perfectly for the dust-size, surface-sown seeds. It also works for tomatoes, peppers, herbs and the like, but may take more sprays to adequately soak.

I have also made garlic "tea" and used that to water plants. It is antifungal and antimicrobial, but it doesn't smell as sweet as the chamomile. Works like a charm for me, though!

Finally, you can sprinkle some cinnamon on the surface. I haven't tried making a cinnamon tea, but I would think that should work too.

The thing I really like about the spraying method, particularly for small seeds in alot of soil, is that you can wet the area where the seeds are, instead of needing to soak all the soil. If the seeds in these kits are planted in the pot they're to eventually call home, it's usually going to be so much soil that keeping it evenly moist will cause exactly what is happening to you.

Gotta get going with the drainage part, though. I HATE it when kits don't have the right stuff! If you can't add drainage holes, at least put some wicks in to help evaporate--strips of newspaper sticking out will wick moisture up and out of the soil so it can dry a bit--it won't look pretty, but it'll get the job done. Also, maybe turn a fan on low and direct it (not TOO close) over the soil.

Good luck and let us know how it turns out!