Hello Shabana,
running the sample database locally is no problem as long as you're connected to the internet.
The error message sounds like there's a problem with the public/private keys.
I'm not sure if you have pasted the public/private keys at the right place? The custom control has some custom properties to do some configuration. For the p/p keys you'll find (@see: page 6 in readme.pdf):
RecaptchaWidget > PrivateKey and
RecaptchaWidget > PrivateKey
In the sample.xsp I filled in "???" as a placeholder. Please replace them by your own keys.
HTH
Please let me know if this solved your problem!
Marco