How to fix Windows is not genuine problem

>> I don't have the origination Key
I believe  you should have, when in doubt, call Microsoft, they will help you over the phone.

You could also just use the PC manufacturers factory restore utility to return the system back to the state when you bought it.

I've had the same issue a few times, calling is easier than restoring (and making backups etc).

there's an MS Knowledge Base, page on that error with several Resolutions
http://support.microsoft.com/kb/929826

What's changed, or not? While you've probably checked, consider possibility of personal install or upgrade to Windows that expired before registration - is it your desktop or one you support, does this use client based on server such as terminal server?

Try booting to standalone without networking, which does not require DNS (or server). Standalone should permit things like changing dates and rolling back to prior configuration.

Nothing changed.  I was working on it for a year.  All of a sudden its just decide to complain.  Client based install.

More info on "More information: DNS name doesn't exist.": this is a total bogus message. Had this several times in my career and each time, the product key was mistyped :) I have no idea why Microsoft will return this message instead of telling you your key is simply wrong.
So a reason could be that your key (which is saved in the registry) is corrupted and needs to be re-entered.

also check date and year - often that's the cause
it can be caused by a low bios batter -if so replace it with a good cr2032

Time/Date is correct.  

I bought it form the downsized company.  They were eliminating their office along with all the equipment.  Now, after 6 month, no one to ask.

have you searched the whole case to make sure there's not a COA sticker hidden?  I've seen them inside more often lately, or under batteries on laptops.  or inside doors, place to protect them from being worn out, it's almost worse to have a sticker you can't read. than none.

but Bottom Line is there's no Sticker, you don't have a copy of the COA Key, you're sorta just stuck "getting legal".

You might try something Like Majic Jellybean to find the key in the filesystem/registry

This is a laptop.  No stickers unfortunately :(

call Microsoft, it's a slim chance they're gonna fix it but if a service pack or critical update broke it, they don't charge for support.

Tried Magic Jellybean also.   No luck.

Is there a way to change the Windows not to look for KMS server anymore?  

Magical Jelly Bean Keyfinder finds a key.  But after trying to enter it, Windows Activation still throw same error code.

Also, forgot to mention.  This is a Windows 7 Enterprise edition version 6.1
Build 7601, SP1