Is there any free OCR API for .NET?

CAPTCHA is NOT a problem, it is a solution (a somewhat silly one) that tries to verify you are human and not some program trying to get access to the page.

The reason why the web site is using CAPTCHA is to prevent the outside world from exactly doing what you are trying to do.

The best way to continue is to ask the owner of the web site for a web service that allows you programmatic access.

If you are the owner of the site just remove the CAPTCHA or add your own web service.

There is tessnet2 which is based on tesseract.

Free and open source.

Will it solve the problem? Maybe. Depends on the CAPTCHA.