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"Error #0" is a message produced by the underlying Adobe AIR software, rather than Market Samurai itself. By itself it doesn't tell us exactly what's wrong. There are a number of potential causes, so we'll step you through the various fixes in order of their likelihood.
#1: Your user account has restricted access on your computer.
The most common cause is that you are using a restricted access account on your computer - and the restrictions on your account are affecting the installation of Market Samurai.
You can find detailed instructions on checking and adjusting this here: http://goo.gl/L7sHB
After this, try installing Market Samurai again.
#2: The User Account Control (UAC) may be turned off
(this will affect only users with Windows Vista, Windows 7 or Windows 8)
This can be checked by going to "Start" > "Control Panel" > "User Accounts". From there, open UAC and make sure it's enabled. (On Windows Vista it's a simple checkbox; on Windows 7 and Windows 8, the slider should be set anywhere except the bottom-most setting)
More detailed instructions are available -
Windows Vista: http://windows.microsoft.com/en-AU/windows-vista/Turn-User-Account-Control-on-or-off
Windows 7/Windows 8: http://support.microsoft.com/kb/975787
Then retry the installation.
#3: Corrupt Installation File
If those measures don't work, then you probably have a corrupt download file. To resolve this issue, please follow these steps:
Go to http://support.microsoft.com/mats/Program_Install_and_Uninstall/en-us to run "Microsoft Fix-It", which is designed to clean up problems which can get in the way of uninstalling and reinstalling software.
As an alternative, download and install "Revo Uninstaller" which is available on a free 30-day trial from http://www.revouninstaller.com/revo_uninstaller_free_download.html - use this on it's highest setting to completely uninstall Market Samurai and Adobe AIR, traces of which which may be hanging around and blocking a proper reinstall.
Perform a search on your hard drive for all files that end in ".air" - delete these, as your computer may be caching the corrupt file, preventing you from downloading a new copy of the file (here's an illustration of how to find the Search feature http://goo.gl/q0inI on all versions of Windows)
Be sure to check that there are no AIR (files with the extension .air) in C:\Program Files\Common Files\ - delete any you find. And clear out any temp files that you can in C:\Users\[your username]\AppData\Local\Temp - it's likely some won't let you delete them, but get rid of as much as possible.
Download the Market Samurai AIR file again from your personalised download page - use the link under option 2, Manual install - and try reinstalling again.