All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If after being hit by a vehicle the goat is still alive and moves, like moving her tail or leg or blinks, then it is permissible to slaughter it and eat it, if you reached it when it is still in this condition, as Allaah says after mentioning the kinds of animals the flesh of which is forbidden for us to eat (which means): {…and that which has been killed by strangulation, or by a violent blow, or by a headlong fall, or by the goring of horns and that which has been (partly eaten) by a wild animal-unless you are able to slaughter it, (before its death).}[5:3]. Ibn 'Abbaas commented on the expression 'unless you are able to slaughter it' that it means slaughtering it while it is still alive, and you can eat it as it is slaughtered according to Islamic rites.' Moreover, 'Ali said: 'If you reach the animal that is killed by a violent blow, or by a headlong fall, or by the goring of horns while it still moves its front or back legs, then you can eat from it.' In another narration, it reads: "If it moves its tail, or walks, or blinks, then eat from it."
As regards when the animal is still alive but does not move neither its front or back legs, nor tail, then the scholars differed whether or not it becomes permissible to eat from it after slaughtering it according to Islamic rites.
Shaykh Al-Islam Ibn Taymiyyah said: 'The (most) correct opinion is that if the animal is still alive and was slaughtered, then it becomes permissible to eat from it regardless whether it was moving before slaughtering it or not, as the movements of an animal that is to be slaughtered cannot be controlled and checked. Some animals make strong movements for a long time, but the movements of others are weak and do not last for a long time. Therefore, whenever an animal that is slaughtered splashes out blood like the animal that is slaughtered when it is alive, it becomes lawful to eat from it.'
The view which says that it is permissible to eat an animal that is killed by a violent blow as long as it is still alive even if it gives only small indications about its life, is the view of the Hanafi school and this is the Fatwa they provide in this regard. This is also one of the views of the Hanbali school and others. However, to be on the safe side, it is better not to eat from the animal that has very small indications of being still alive when hit by a violent blow. But if (in principle) you doubt whether or not the animal is alive, then it is more appropriate to avoid eating from it as many scholars are of the view that if we doubt about the life of an animal, slaughtering it does not make eating from it permissible.
Allaah knows best.