Have you been targeted?

I got a call today on a seldom used phone line. <red flag #1>
The calling number was blocked. <red flag #2>
I answered. There was a 2-3 second delay before being connected. <red flag #3>
"He" asked if he was talking with "Kevin". "He" had an East Asian accent. <#4>

He was part of a Windows support team. When I surf the Net, my browser downloads many malicious files. Their Windows server had been notified and he was going to help me to remove them.

He gave me step-by-step instructions to open the Event Viewer. He pointed out all the errors and warnings caused by malicious files. He asked me to go to www.support.me where his technician would connect to my computer and help me remove the files - at no cost to me. <#5, #6, #7,...>

I decided to play along...

He asked me to enter the support PIN I got with my computer. I told him I didn't have one so he gave me one (Of course I didn't enter it). Then I asked a lot of dumb questions. He put me through to the technical support supervisor. More dumb questions... They had plausible answers for everything. Finally, the supervisor put me on hold while he checked something and the call was dropped a few seconds later.

I know a number of end users who have easily been taken in. These guys are convincing.

Has anyone you know received similar calls or been taken in?