If some site violates Google TOS, it is very possible it will get banned. The most common reasons are: hidden text, link spam, link farm. If your site does not apear in Google, there is a simple way to check if it is simply not indexed yet, or if it has been blacklisted.
Go to www.google.com and type the site name in the search bar (let's take testdomain123.biz for example).
If you get an answer like this:
Sorry, no information is available for the URL testdomain123.biz
If the URL is valid, try visiting that web page by clicking on the following link: testdomain123.biz
Find web pages from the site testdomain123.biz
Find web pages that contain the term "testdomain123.biz"
Then your site is not banned.
BUT
If you get an answer like this:
Sorry, no information is available for the URL testdomain123.biz
Find web pages from the site testdomain123.biz
Find web pages that contain the term "testdomain123.biz"
Then your site is blacklisted.
Note the line If the URL is valid, try visiting that web page by clicking on the following link: which is the difference between two cases.