When was the first computer that ran on DOS invented?

Answer 1

"On August 12, 1981, IBM introduced its new revolution in a box, the 'Personal Computer' complete with a brand new operating system from Microsoft and a 16-bit computer operating system called MS-DOS 1.0."
http://inventors.about.com/library/weekly/aa033099.htm

This other webpage has a more detailed history of the development of DOS: http://www.patersontech.com/Dos/Softalk/Softalk.html