Rebooting will not un-install the malware they installed when they were in your computer. You need to recover an older version of your system or take your computer to a reputable local computer repair place and let them do it.
My neighbor fell for it. After I told her it was a scam she took her computer to be repaired. They discovered that the scammer turned off her anti-malware.
Received a call from this number, they claim to be calling from 'Windows Technical Department". I was highly entertained by this scam and kept them on the phone for several minutes and eventually was put on with a supervisor who by the end of the call was berating me and calling me nasty names. At various points they claimed to represent Microsoft and then at other times they claimed they did not represent Microsoft. They also asked for a credit card number before I gave up and hung up on them.
Same experience as Brian. "Windows Technical Department" - I bet not. I'm sure that they would offer to examine my hard drive at the same time as they downloaded all my stuff into their computer.
These people claim to be with Microsoft. The have gotten to a few a my friends. They have very thick accents with the names of Mike Taylor and Christine Johnson. The get very abusive and threatening when they don't get what they want.