Good Morning Anne, 

Thank you for contacting the U of M Extension Service, 

Please click on this link from the U of M Extension Yard and Garden website: https://extension.umn.edu/planting-and-growing-guides/starting-seeds-indoors

There are many factors that could be affecting your plants. Are you using artificial lights? Did you use sterile potting soil? Were the containers clean?  It appears to be some sort of fungus. 

In the current weather, you could put them outside in the sun for a few hours and see if it improves. If not, it's not too late to start some new plants. Tomatoes germinate in a few days. 

Even though your plants are tall and stringy, you can plant the tomatoes deep, leaving only a few leaves above the soil line.  They will sprout roots from the stem. 

Good Luck!