First thoughts, the pot isn't big enough and it isn't getting enough food.
Pot needs to be 4-5 times the size of the rootball to give the roots room to grow and it needs feeding throughout most of its growing season (spring & summer).
You say you've used the right compost, right light etc but can you tell us what you mean by 'right'.

Thank you I will change the pot today. Advised by person who is successfully in growing Aloe she advised aloe compost. It grew continously over winter and I have never fed it as I assumed it would get nutrients from compost. Can I feed with Miraclegrow. It is not in direct sunlight but is kept in a light area, not in draughts. Thank you for your advice.

Looks too lush and spindly to me for Aloe vera,which should be chunky, but same rules apply for any aloe. As I said before I would keep it a lot drier and put it in full sun. . It needs a very light gritty compost - cactus compost would be good. I neglect mine, haven't repotted it for a long time and hardly ever feed it - maybe you are kiling it with kindness? It can get by with hardly any water, especially in winter. If Aloe vera is really short of water the leaves start to look pale rather than droopy. They are designed for very dry areas and hot sun where they will go for months with no water at all, and the more you can reproduce that the happier it will be. You can see what overwatering did to the roots in your original photo! Once a month is plenty in winter, and even then be a bit mean with it.

Regarding feeding - doesn't need much, a balanced fertilizer 2 or 3 times a year is more than enough. Best not fed in winter though. Yours is definitely alive - just looks like it needs a good dose of strong light/sunlight and probably less water at the moment. Best repotted, if necessary, in late spring, and let it dry out for a week or so before you do repot it.

I have the same one and nearly killed it off last summer by drowning it, poor thing was down to only a couple of very small shoots, all the rest were yellowing and very limp, I cut away all the limp stems but didn't repot mine, all I did was top up with compost and moved it into the kitchen windowledge, it gets no sun until very late in the day even in the summertime, only a trickle of water about once a month at the moment and no food at all, I was killing mine with kindness, its recovered well and is a very healthy looking specimen now.....