A caller made a claim to be from Microsoft. He said my computer was hacked or had vulnerabilities, and asked to get an access to my computer in order to fix the problem. Should I let them access my computer?

This is a typical SCAM.

Never ever let anyone access your computer in a way where they made the contact with you first.

In this particular case, Microsoft is explicit in that they never call people around. Microsoft says: “Neither Microsoft nor our partners make unsolicited phone calls (also known as cold calls) about your computer security or software fixes.” More at Microsoft’s Cyber Trust Blog:

Is that call from Microsoft a scam?

If you have already fallen to be a victim of such a scam, Microsoft goes on with what should be your next steps:

What to do if you’ve been a victim of a phishing scam

Here is another of our articles that covers similar “scam” scenario:

Why did Norton charge me for support?