Hi,
Could you try the following steps on your machine and see if issue gets resolved:
1. Go to command prompt, right click and choose "run as administrator".
2. Type sfc /SCANNOW and enter. The scan would take some time.
3. Once the scan is complete type msiexec /unreg and press enter.
4. Type msiexec /regserver and enter.
5. Once you are done with the above 4 steps try installing Adobe AIR again.
If you still face any issues let us know.
Thanks!