There is no such thing as verifying URL for existence. You can only verify it for validity, i.e. compliance with the URL format. After that there is no verification.
If a server does not recognize a certain URL, it will typically generate a 404 error, which may or may not be the recognition of its validity, because some URL-s can simply expire, some may fail to be served because of a server problem at the moment, some may simply not like your locale or your IP address, etc...
Calling
InternetCheckConnection
isn't gonna help you much here, it mainly does what it says, checks your internet connection, but this isn't what you inquired about. Although it does verify whether it can open the URL, it is secondary for the call, and may fail, for instance, on URL format validation. But even if it succeeded, it would be no indication of the URL being valid for reasons already described above.
You need to narrow your search to something more meaningful.
Examples:
- If you want to verify that the URL refers to an existing file, try to open and read that file.
- If you want to analyze the server response to the URL, just read and parse the response.
- If you are dealing with a custom URL that you expect in a certain format - check it locally.
and so on. And if you publish a new, better defined question, I'd be happy to answer that one ;)