Just had this same experience.  I asked where she was calling me from, and she said something I could not understand.  I said this is a bunch of crap and a scam!  She hung up on me.

got the same type of call today--and my wife said she had several in past few days with similar request.  "Your computer is infected...., are you at your computer?"  Said he worked for Digital Network Services, with an 866 telephone number.

My wife just had this call.
The primary reason to know this is a scam is because even if your computer was infected with somehting and atatcking someone else's servers, they would not have your contact details, all they would have is your IP address then they would only be able to track that back to your ISP and contact them, and your ISP would then be the one's to contact you, as they are not allowed to give out your personal details.

Just had the same company try this on me in the UK..Indian accent, however working as a CIO I knew my personal PC was protected etc.. so after asking a few questions they hung up.

stay safe peep's and tell your friends

Same exact scenario.  Showed up on my cell phone as Unknown.  Same accent as above.  Wanted me to log into my computer.  I told him I was at work and he asked for a time to call back.  He added a little hook.  He told me that I should stop doing online banking until he could help me fix the issue.  He was pretty good and getting better.  I'm sure a lot of people get hooked into this scam.

I do not have call display. A man with an Indian accent claiming to be Noah Tyson from Digital Network Server somewhere in Brampton, Ontario just hung up on me when I had the audacity to tell him that I felt certain he wasn't on the level.

"Noah" claimed that their server was getting messages from my server and refused to tell me what my IP was. He just kept insisting that he needed to know my computer ID. I kept asking him how he knew it was my computer if he needed to know the ID number.... He told me my name and address (as it appears in the phone book). Well, duh. We're not unlisted.... When I asked for the address of his company, he told me it is secret(!)

He seemed to be somewhat perturbed when I laughed at him at that point. What was most interesting is that he never denied anything when I suggested that he was not on the level. After hearing a repetition of "No, you tell ME what our ID number is", he suddenly ended the call by saying, "Good bye. Have a good day" and hung up on me.

On Nov 1, 2012 I had the same call but I don't have call display.  He was an Indian speaking man who said his name was Charles Brown.
He said he was from Digital Network Services, a government service, located in Brampton, Ontario.
He also said the same as previous comments, that they had had complaints from our IP address and we were blocking a bunch of computers. He wanted me to go to my start menu so he could tell me how to fix it.I was suspicious so I told I couldn't do that right now and asked for a number to call him back. He asked me when he could call back but when I asked for his number to call him he gave me 347-329-4401 and said he was in Brampton, Ontario.
When I searched Canada Better Business Bureau I found this page.

On October 29, 2012.  I had the same call, BUT ON THE PHONE IT SHOWED UNKNOWN CALLER.  HE WAS AN INDIAN SPEAKING MAN.

HE SAID THAT HE WORKS FOR THE GOVERNMENT OF CANADA FOR THE DNS.  HE TOLD US THAT THEY HAD COMPLAINTS FROM OUR IP ADDRESS AND WE WERE BLOCKING A BUNCH OF COMPUTERS.  HE WANTED US TO TO TYPE IN THE INFORMATION THAT HE GIVES US IN THE START MENU OF OUR COMPUTER.  BUT WE DID NOT

WE WERE SUSPECIOUS AND ASKED HIM FOR A NUMBER WHERE WE CAN CALL HIM BACK.  HE TOLD US THAT HE WAS IN CALIFORNIA.  347-329-4401.

I THEN CHECKED THE NUMBER ON THE INTERNET AND FOUND THIS THANKS FOR THE INFO.

Be very wary when talking to these folks!
A man with a Indian speaking accent phoned me up last week and my caller ID showed the call as a Number Blocked & Name Unknown call. So I immediately thought it was another telemarketing call since they typically use blocked numbers.
He claimed to be calling from a company called DIGITAL NETWORK SERVICES.
He claimed that computers hackers were trying to break into my computer through their corporate computer servers.  Whenever someone with an Indian speaking accent calls me up out of the blue and wants to talk to me about computer hackers, I immediately become suspicious!   So I asked him to give me his real phone number. He said his real phone number was 347-329-4401 which is in New York city.  Recently a number of computer hacking outfits from India have been trying to shake down computer users here in North America for the purpose of extorting computer hacking "protection" money from them.
I have experienced this kind of thing in the past so I told him to call me early the next morning.
He never did.  So be wary when dealing with this outfit. They may very well  be crooks!  Tell them to call  you back early the next morning, they usually never do. I can only assume that they do not want to be identified or tracked.  Hope this helps you.