If you just picked a random tech support company to call, there are quite a few that are setup to just take money and pretend there is something wrong. Not saying that there is not, but often the hackers are those same companies that you invite to use your computer.
First, get a router, do not just connect the computer to the modem, unless the modem has a router built-in. You can have the ISP change your IP for you. And re-installing Windows will clear most viruses.