[Patricia]

I think I would personally repot them into some other pots rather than the paper ones and make sure to put them were they are warm. Barring that I would start again. I plant my tomatoe seeds in a recycled flat veggie tray with a clear bag over until they germinate and then pick out and start potting up. Only to the next size pot that they will fit into for a week or two and then pot up to the next size. And making sure they keep warm, either in my conservatory or the mini green house. I did start my seeds back in February, and they are now out in the garden in grow bags.  I think I read where someone starts theirs on New years day. And like David says I always plant them deep into the pot. This makes them stronger. Best of luck.

[Jay The Digger]

They do look a bit wet don't they.  I agree with all the posts here.  Replant in better compost up to the lower leaves, put somewhere warm and bright, yet airy.  A window sill is fine.  Introduce them to the outdoors when the poor chaps are bit bigger.  

I have always found that by letting the top of the compost dry off before rewatering I keep that fungus at bay.  I always water from below so the main stem doesn't weaken or rot.  It also encourages a good root system which determines how good your crop will be.