How can I purchase Mountain Lion on a computer and install it on a different computer? I bought a used MacBook Pro 15″ with Lion and Windows dual boot. I accidentally dropped my Mac when it was on - everything was fine until I rebooted it and it got stuck on the grey screen, and I lost the dual boot so even Windows wouldn't start.

I've searched on the web, and it tells me to restore it via the internet with ⌘ cmd+R.

I did it, but it asked me to update to Mountain Lion, so when I hit ok it says that my Apple ID has not been used to purchase Mountain Lion.

What can I do to purchase a new copy of Mountain Lion with my Apple ID? Can I use my other PC to purchase it with my ID, and after that download it when am in recovery?
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.