There are a lot of factors in starting indoors.
1) Light.
By experience, I figured out nothing can bit natural light from the south/east window PLUS a lot of artificial light added. The sun only works well for very short time - then it either gets too high and covered by roof or blocked by the window frame or just moves... However, it is very important. I gave up north/west windows few years ago, and started to get much less problems after that.
Artificial lights are very important too - cloudy day, early morning, early night... The plant need 14-16 hours of sun to grow well. That means they need night too, so I am using timers to turn on and off my light system. I have two different kinds - all home made. One set up uses 23'' cheap grow lights from Walmart, 8 of them fixed on 23 '' square frame. Whole construction is hanging on the ropes, so I can change the position of the light as plants growing - it is important to keep the light just about 2 inches from the plant tops. The second set up includes cheap light fixtures from home depot for single spiral bulb. I bought fluorescent photo bulbs, they are pretty powerful... 6 of them are fixed on the frame in 2 rows and covered with a large mirror to spread the light. The color temperature of the light is very important. Again, by experience I figured out that 6500K+ does the best for indoor starting(meaning you will plant them outside later). As plants grow, you take light system more and more up. It means lower portion of the plant receives not enough light - my plants could be a foot tall by April here, so as soon as weather permits, I set up portable greenhouse on the deck and take them out. it means heater at nights!(Ouch)
Light related issues: leggy plants, oedema (over-watering contributes here too)
2) Temperature.
All plants need different temperatures to grow the best. Peppers like it very worm. Tomatoes like it cool. And so on. This could be a major problem when you grow them all together. So I have 4 stations - one is very warm spare bedroom above my boiler room, another one in my kitchen near deck door and the last one in the basement bedroom(with window) where I keep 55 degrees all winter long as nobody lives there.
3) Soil and pot size. One of my latest notes for myself - do not use peat moss based mix on peppers. It is to acid for them - they doing much better in coco-fiber based mix. I use half gallon pots - this give the plants time and space to grow from end of February till mid-May. My mix includes
2 parts of coco-fiber(peat-moss for tomatoes instead),
1 part of sanitized strait horse manure(no bedding) compost,
1 part of perlite
1 part of vermiculite
slow release fertilizer
4) Water. I always over-water and then feel sorry for my plants. I am getting better and better each year. You stick your finger in the soil and it is DRY!!! But you do not go deep enough.... So I use sensor that I stick in the soil when I can't decide.
Over-watering is the door to fungus, dumping off, suffocating plants and oedema.
5) Other
Every plant type has it's own requirements. Tomatoes appreciate fan. Eggplants and peppers need support on 4-6 leaves stage. (plastic stick from fruit arrangement and trash bag tie works perfect)

I know that everybody has own ideas and experience. I do not try to direct you what to do - just share what I learned for last 7 years of starting plants indoor)

Check out all the FAQs and info on the Growing from Seed forum here.

Dave

What is it you are trying to start so early?

Thanks for your post Galinas!

floral_uk I'm not starting anything yet, just preparing to try and figure out what I am doing wrong for next month/the month after.

If they look burnt, it's possible the lights are too close and/or on for too long. I've had that happen, although the plants usually grow out of it.

Can you show us some pics.

Here is a link that might be useful: growing seedlings indoors

Sounds like it might be a soil problem. Your problem sounds like it's not just that your seedlings aren't growing, but that there is something actually hurting them. It's hard to overilluminate indoors, and if you under-illuminate, things will just grow more slowly. What are you using for a planting mix?

I'll echo floral_uk's question. What exactly are you trying to grow that you're having trouble with? You say you can get seeds to start, but not grow. Which seeds?