I am not an expert but mine is outside in the sun and growing great. Maybe you could gradually introduce them to more sunlight?

Pat

I would like to know if I can replant Basil? I was given some plants with the roots still on and they were in water

I'm only starting my second year gardening, but a friend and I played with basil this year.
She grew several plants from seed. She put 2 in the ground, kept 6 in pots and gave 2 to me. The two she gave to me were nearly dead, but I transplanted them to a larger pot and they lived (and produced enough for my needs). The 6 she kept in pots did ok, but the 2 she planted in the ground turned into basil bushes.
Basil seems to be very picky about water requirements, so if you keep it in a pot be sure to water it regularly. I don't know what soil/fertilizer she used for her pots, but mine were unfertilized. I think the bed she planted her two basil bushes in has naturally good soil. All of ours were planted in full sun.