The primary problem is the peat pots. Lots of discussions here about all the issues with them but basically it boils down to they create overly wet growing conditions that causes root rot and stunting.

Had you transplanted them out of those into any small plastic container with a basic potting mix most would have recovered and done fine (assuming you didn't over-water them).

Second, would be the temperature in the area. Seeds need heated soil to germinate but once sprouted they must be removed from the heat and grown in cool conditions 60-65 is the ideal but 45 it way too cool for tomatoes. They will tolerate 50-55 for short periods but not less. You'll have to provide some sort of heat to the area or enclose it in some fashion so at least the light fixtures can keep it warmer.

Next time skip the peat pots and you'll have much better results. If you must use them for some reason then you have to VERY carefully monitor the soil moisture levels and reduce watering substantially below normal.

Dave

I don't know about peat pots, since I can't remember the last time I used them, but that soil doesn't look soggy. If that's a soilless mix you're using, then yes, you need to start providing some nutrients. 45ú is ok for some seedings, like lettuce, but not heat lovers, which get stressed at those temperatures.

I no longer live in a climate where I have to keep seedlings indoors for extended periods of time, although I don't live in a particularly warm climate either. I just got sick of the whole high-humidity-sterile-soil-heat-mat routine, and now I just sow directly into potting soil in plastic cups, providing no plastic covering or increased humidity or heat, just keeping the soil moist, and occasionally spraying with a bat guano/earthworm casting solution or sprinkling a little dry organic fertilizer on the soil if the seedlings are large enough to water normally. I do this with vegetables, herbs, flowers, shrub seeds, everything. So far I have better results, but that's me, here, in this climate, in these conditions.

I don't fertilize much before transplanting, but I do find that some added nutrients to a soil that already contains some composted material is of benefit, and doesn't weaken the plants, as long as there is good light. A seed really just contains enough nutrients to get two leaves in the air, and a root in the ground, so beyond that you're going to have to provide something more, either with potting or actual soil, or a drink of fertilizer.

I had a similiar problem and it had nothing to do with peat pots. Many of the soilless mixes don't have any nutrients, so you need to add some to boost the seedlings along (and some of them that have fertilizers in them I've heard negative things about). Anyway, my seedlings were in plastic where each section was 9 plants. They germinated, and then stopped.

When you fertilize use a very dilute solution. Mine is more dilute that the weakest dilution the fertilizer I'm using lists as a mixture (a 'Miracle-gro 'like' fertilizer).