Yep, sounds like the connection between the key and the actual switch is no connected.
Where the problem is, is not as obvious. It can be at either end of the rod. As I remember, the actual switch is in the box mounted on top of the steering colume at the bottom.
If you can get under there and watch while someone turns the key, you may see the problem.
Its unlikely that the actual rod broke, but anything is possible. Probably something broke where it hooks to the switch or the rack at the key end.
If you can see the rod at the switch, and it does not move when the key is turned, then its probably at the top.
