Does a greenhouse help to grow better seedlings?

Hi,
I am very interested to grow holy basil (tulsi) from seeds.

But everytime i try to grow them, they either wont germinate, or they wont grow more than 0.5 cm(literally) height after 4 months. I have tried growing them in winters (minimum temperature of 60 deg F), summers, all temperatures.
But never succeeded to get anything more than 1cm tall plant. Low light, high light, direct light, indirect light, tried different sets in different ways. Tried misting daily, misting twice, covering the soil to keep it humid, but never worked.

So the current range outdoor temperatures are min - 75 deg F to max - 105 deg F. The location i prefer to grow as of now gets around 3 hours of direct sunlight (9-12), otherwise its very bright with indirect sunlight.

I was wondering if a green house like this can help to grow seedlings in a better way
http://www.ikea.com/ae/en/catalog/products/70186603/

Or there is something i am seriously missing?

Just for information, i obtain the seeds from the current two holy basil (tulsi) plants i have.

That to me, looks like a good thing to have to start seeds. But I don't think it would be any better than what you have tried. I have never tried holy basil from seed and I get few sweet basil seeds to germinate and grow big enough to have more than 2 leaves. Keep researching and trying. Maybe someone with more experience could help you. Have you tried different types of medium? Paper towels, cotton balls, vermiculite, peat, etc.? Do the seeds need to be stratified?

In my experience, Basil, like so many other herbs, likes the Mediterranean climate, plenty of heat and light. I start them inside, and always got decent germination, but the seedlings didn't develop. I used a popular commercial seed starting mix that contains time-release fertilizer, nothing special. When I started using T-5 fluorescent lights on a timer set for 14 to 16 hours a day, I had much better luck. I ended up with nice sturdy plants. I think you have the same problem, 3 hours of sun doesn't seem like enough.

Good luck!