Hi Alex,
I think the error you are getting is that your computer either does not have iTunes installed, or that it needs to be uninstalled and then installed using the latest version from Apple.com. Make sure your computer has the software. You should be able to open iTunes on your computer without the iPhone connected to it by clicking its desktop icon. FYI: I do have the Apple Mobile Device Service (AMDS) software on my computer (Windows) and it shows in my Programs and Features.
There was a fix some time back when iTunes failed to launch properly. It involved the following steps:
Check your DOWNLOADS folder for iTunesSetup.exe and delete it if it is older than a month or two. Download fresh from Apple.com the latest version of iTunesSetup.exe but delay installing it. Then....
Go into your "Uninstall a Program" in Control Panel. Uninstall iTunes. Uninstall Apple Application Support.
(From this point on until we reinstall Apple Application Support, neither QuickTime nor Safari 4.0.4 will be able to run.)
Next we'll remove any leftover program files and folders.
(1) Open "Local Disk (C:)" or whichever drive your program files are stored on.
(2) Open the "Program Files" folder.
(3) Right-click on the iTunes folder (if it still exists) and select "Delete".
(4) Open the "Common files" folder.
(5) Open the "Apple" folder.
(6) Right-click on the Apple Application Support folder (if it still exists) and select "Delete".
Now empty your Recycle Bin and restart the PC.
****Reinstall Phase****
After the PC restarts, do not open any other applications. Disconnect from your network and/or the internet. Switch off all your security software (firewall, antivirus and antispyware).
Now start the install by doubleclicking the iTunesSetup.exe file you downloaded earlier. It should be in your DOWNLOAD folder. Let it install a shortcut icon to your desktop.
Reenable all security software prior to reconnecting to your network and/or the internet.
Did the install seem to go through okay? If so, does iTunes start launching properly again when you start it from the desktop icon?
You will also need to create an Apple I.D, if you haven't already, if you plan to download any of the Apps from the App Store or any music from iTunes Store, or use the backup feature of iTunes. You can do that most directly at apple.com.
Good luck