What brand of vga cable did you get?
Did it work before? Does it work with a different TV/projector? Did it work with ios 7.x? Are there other A/V input ports? Try all others. Check settings.
Anyway, with the introduction of ios 8.x, apple stopped supporting older a/v cables. You need to get the latest a/v cable with the correct firmware. There is a little chip in the a/v cable. go to the apple store. Buy a new cable. Verify the cable works in the store.
Here is one reason I heard for the switch in cable requirements: fire! See a picture in this discussion:
https://discussions.apple.com/thread/6886734
What cable do you need for your ios device?
https://support.apple.com/en-us/HT202044
Go wireless:
https://www.apple.com/appletv/