He wants remote access to your computer to scam you and steal your identity. His claims of receiving error messages or that they were told by Microsoft to contact you to fix your computer are all lies designed to get you to grant remote access.  Once he has that, he has complete access to everything on your computer and while "fixing" it will be able to download the entire contents of your hard drive to search for personal information such as credit card numbers and login names and passwords to online sites you routinely use.  These criminals also will load malware that allows them access to your computer any time you are online which they can then use for all sorts of illegal activities that will trace back to you. Never allow anyone who cold calls you to have remote access to your computer.  Microsoft has a webpage with warnings about this type of scam.

http://www.microsoft.com/en-gb/security/online-privacy/avoid-phone-scams.aspx

Received a call from a man who sounded as if he were from India.  He stated that I had not responded to their many requests to repair my computer, and that he was there to help.  Sounded fishy.  Asked him to call back in three hours.  What is he up to?