Does anyone know how to see if a website is banned from google search results?

Type the entire url in the google search bar (use www and/or htt://www). If no results come up for the website and it isn't new (hopefully you know if it's been indexed and cached in the past) then you can figure there is a problem.

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Southwest Chicago Suburbs Real Estate is an affordable area with close access to downtown Chicago. Money Magazine says that Orland Park real estate is one of the best places to live in the U.S. Next door you can find Tinley Park homes for sale and get Orland Park amenities at a more affordable price.

Not at all.
It happens that a website can just disappear for a while and then appear again.
So that doesn't answer a question if it is banned or not.

I didn't say the fact that your site does not show up on the index means you are actually banned. I said there is some kind of trouble if your site was in the index and now is not.

I believe if your site no longer appears in the index then you need to contact Google to see if you are truly banned or not. But some people think their site is banned when they can no longer find their site in the top 1000 results. They don't realize that if it does show up by typing in their site's url in the Google search box it has not necessarily been banned.

Checking to see if you are still in the index is simply the first step.

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Southwest Chicago Suburbs Real Estate is an affordable area with close access to downtown Chicago. Money Magazine says that Orland Park real estate is one of the best places to live in the U.S. Next door you can find Tinley Park homes for sale and get Orland Park amenities at a more affordable price.

I know that, but...
When Google Page Rank Update starts your website can disappear from both search engine results and url at all.
So I'm trying to figure out if there are any other ways to check it out (if the website is banned).

I've had a page or two get deindexed but never my entire site or homepage.

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Southwest Chicago Suburbs Real Estate is an affordable area with close access to downtown Chicago. Money Magazine says that Orland Park real estate is one of the best places to live in the U.S. Next door you can find Tinley Park homes for sale and get Orland Park amenities at a more affordable price.

I'm not saying about deindex, the website just disappears sometimes, then appears again.
Haven't you ever noticed that?

If one reads this and other forums, I thought it was pretty well know that G is having some problems with their DCs and many sites are rising and falling as the world turns. remaining cool seems to be the best advice.

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Welcome to Colorado Rocky Mountain Real Estate - Explore Summit County Real Estate from Breckenridge Real Estate to Keystone Real Estate.

I wouldn't just assume that G is having problems. They test different filters with the DC's. If you are completely gone from a DC I would take a hard look at some of your practices and see what might be causing it. The filter may never move across all DC's, but what if it does?