What did I do to my sprouts?

I had some sprouts on a wet paper towel for about a week. They started growing fine so I moved them into a dish of plain water. They started to do better so I got the brain child idea to move them into the grow room. Then they threw up on themselves and practically died. The root is all brown and shriveled up so now they are back into a dish of water back to the windowsill.

I know a lot of people use rooting cups, but I cant find them in my area right now. I will continue to look and or order them on the net soon enough, but what can I do to finish sprouting my current seeds before I get a rooting tray? Does anyone have a link to a foolproof DIY sprouting system that I can follow?

once the taproot comes out of the seed, you plant it maybe a 1/2'' beneath the surface of the soil, root down, and water it. do it!