When seeds germinate and then the seedlings wilt and die it could be due to a condition known as "damping off" disease which is caused by a soil-borne fungus. If you used soil from the outdoors the soil may have contained fungus spores. I would start over with sterile soil (potting mix) in clean pots. If reusing the same pots sanitize them with bleach (1 part bleach to 10 parts water). Give your seedlings plenty of heat and light, and be sure not to overwater.
For more information on "damping off", please visit the following link:
Since you successfully germinated the seeds indoors, then they died, most likely they either had too much, or too little moisture, and or light sources were not correct.
The seedlings need to be kept damp. A good soilless potting mix, specifically for seed starting is preferred for starting seeds.
Most indoor lighting is not sufficient for seedling growth, and the addition of grow lights is necessary.
Here are a few links to help you get started.