If the soil was cold and excessively wet, the seeds may have rotted. Dig up one of the seeds and examine it. If it is swollen and soft, the seed has rotted and you will need to start over. If the soil was too dry, the seeds may not have germinated or may have dried up before their roots could take hold. My seedlings are spindly.
Plants grow tall and leggy when there is insufficient light.
Use grow lights and try lowering the room temperature and reducing the amount of fertilizer you apply. The leaves on my tomatoes are starting to look purple along the veins and on the underside of the leaves. If you have been using a dilute fertilizer for the first three to four weeks of the seedling s life, it may be time to increase the fertilizer to full strength. My seedlings were growing well until all of a sudden they toppled over at the base. When the stems of young seedlings become withered and topple over, they have probably been killed by a soil-borne fungus called damping off.