These are indoors? I think they most likely are not going to work for you.
Sounds most likely like damping off. It's a fungus that little seedlings are very vulnerable to especially in conditions of high moisture/humidity and low air circulation. The seedlings get spindly, they get a little pinched in area right around the soil line and then they flop over. Once they are lying flat there is nothing you can do but pitch them and try again.
Are you trying to start them in peat pots? Pitch those too, they are terrible, and get plastic pots or just plastic drinking cups with holes put in the bottom for drainage.
At this point, I'd start them outdoors. You can still do it in pots for extra control, but leave them outside for air circulation. If in pots water from the bottom only (set the pots in a tray and put A LITTLE bit of water in the tray and let the pots soak it up).
Don't bother trying again with the cauliflower yet; it is too hot for it. Cauliflower is a cool weather crop. I start mine indoors mid Jan and plant it in the garden mid March. (Well actually I don't grow cauliflower, but that's how I do broccoli and they are closely related.) Save the seed and start it late in the season for a fall crop.