How can I purchase Mountain Lion on a computer and install it on a different computer?
If you dropped your computer and it stopped booting right after that, you may now have a defective hard drive. I do not recommend attempting to re-install the operating system (Mountain Lion), as this may cause data loss.

My current recommendation is to confirm that you have a good backup of the data that is on your computer. If you do not have a backup, it may be necessary to attempt data recovery from the drive that is in the machine.

If you do have a current/valid backup of your data, I would recommend attempting to boot from another disk (CD/DVD, USB flash drive, etc.), and attempting to open Disk Utility to see if the software is reporting SMART failures with the drive. Alternately, very poor performance or clicking sounds while attempting to view/access the drive may be indicative of a defective drive.

Regardless, at this point, a system re-install is not likely to help with your issues (based on the problem description). If you are at all concerned about data loss, or are hesitant to attempt diagnosis/troubleshooting of your machine, I would recommend taking the machine into an Apple Authorized Service Provider or Apple Store for further assistance.