You need to look at the specs for that model of MacBook Air you are planning on purchasing. It will tell you the maximum storage ssd it will take, which on most MacBook airs is 220Gb. Also make sure if you get a deferent brand of ssd that it fits in the area for the ssd and it doesn't go over the screw hole at the end. Most likely it's a better idea to get a 120 to 220gb ssd from apple to make sure it's compatible. But if you find a ssd from another brand that's cheaper again make sure it fits in the rectangle and doesn't go over the screw hole.
This might be the problem. If you can take the bottom cover off your MacBook Air, there is a small sized board to the right of the laptop when you are looking at the bottom with the cover off. There are 2 wires connecting it to the logic board. One on top which is called a ribbon, and one below it. Take one side of the ribbon of of the board and lift it up so you can see the other wires. Check if there is damage to the wires and or if it's un plugged. I hope this helps!