1 - do a google search for the sites exact domain name 2 - use the site: command. Example - site:www.google.com That will give you all of the pages that google has indexed of your site. When neither search gives ANY results, chances are your banned.
I agree with Kev, however, I've seen sites dissappear before, including my own, only to return a couple weeks later. That will tend to happen to brand new sites, you'll show up in the index for a few days, and then you get dropped from the index. What I think happens is you hit a datacenter one day that has you, and then you hit another datacenter that has not been replicated to yet. So thus it appears as if your de-indexed. Just wait a couple weeks and if you don't show back up in google, then chances are you may be banned.
I searched my site by typing my own domain name and I can find the domain from the search results. However, when I type this info:mydomain.com, It said "Sorry, no information is available for the URL mydomain.com", so, does this domain banned?
Chances are, yes - if you do an exact search for the domain name, and you have been listed with google before, your site might have been delisted. What is the name of the site? I would like to take a look at the site and see what kind of content you have on it and take a look at your backlinks. Being in the so called "sandbox" does not remove your site from google. It just knocks your site way back in the results pages.