W10 pro, what web browser you are using? Have you tried different network? Like test it out in starbucks. This will cancel out whether the issue is your network or it's your laptop.

Once you have established that your laptop is the issue, then you diagnosed further.

Please be more specified like is it using google mail or office 365 or other type of webmail. What ports being used for SMTP. What is the smtp email server URL. What is the domain name used.

I think resolving the issue with browser would be easier because browsers only need to use port 80 or 443 for everything. If the email does not even work in browser it means something else is wrong.

Now that we have established that the network is not the problem then we can proceed with diagnosing the PC issue. Can I know what is the web address you are using for accessing email in browser? If you do not wish for public to know, you can PM me the URL. No need to provide any login details. Just to login page to start with.