I just had a call running along the same lines from this number.
Claimed to be from Telstra technical department. Indian accent.
Tried to get me to download software from "team viewer.com".
He wanted access to my computer.
He couldn't provide any of my personal Telstra info such as birth date or other phone account details. Info that is available to the lowest level of Telstra operators. Claimed he was from technical dept. and that the accounts department was closed at this time.
He became very impatient with my questioning and suspicion.
I hung up. He rang back three times and finally gave up.

just got a call from Alex (he had an Indian accent) - from a company called UTC who quoted this phone number said company was based in Newtown Sydney - no they are not!! He als0 quoted a number that he said was my computer number and only he and I know it!! but he couldn't tell me what brand of computer I had. the scammers never give up do they?

Same call same story - gave me their Number for me to chack them out - asked me to run www.support.me - - this was more informative http://www.techsupportforum.com/forums/f112/support-me-scam-626968.html

Viruses, Windows(r) scams and the like.

I received several calls over many weeks stating I had a virus on my computer which a local technician would not be able to remove and on the last call (after I had repeatedly requested that they send a fax,as they already knew my number) and I slso insisted they give me a contact they gave me the number (02) 8073 0573 to call for computer assistance.
Both Male and Female persons had Indian accent.