Error 1721.There is a problem with this Windows Installer package. A program required for this install to complete could not be run. Contact your support personnel or package vendor.

Hi M.kobessen,

    
1. Does this issue occur while installing all the programs or only with iTunes?

First you may try the steps provided in the below link.
     
http://support.apple.com/kb/HT1926?viewlocale=en_US

Method 1:

Start the Windows Installer service

a. Click Start, type Services.msc and press {ENTER}
b. Double-click Windows Installer
c. Set the Startup type of Windows Installer to Manual
d. Click Start to start the service. Note down the error message if any.
e. Click OK.
 
Method 2: Unregister and re-register the Windows Installer to do that follow the steps provided below.
 
a. Click Start, click Run, type MSIEXEC /UNREGISTER, and then click OK. Even if you do this correctly, it may look like nothing occurs.
b. Click Start, click Run, type MSIEXEC /REGSERVER, and then click OK. Even if you do this correctly, it may look like nothing occurs, or you may briefly see an hourglass. After you run this command, the operation is complete.
c. Try your Windows Installer-based application again.
 
Method 3:

Try performing SFC scan on the computer.

SFC /scannow is a super-useful command you can use in any Windows version. When the SFC (System File Checker) command is used with the /scannow switch, the tool will scan all of the important Windows files on your computer and replace them as necessary.

Missing and corrupt operating system files (like many DLL files) are arguably the biggest cause of major Windows issues. Considering that, plus the fact that SFC /scannow is completely automatic and very easy to use, the tool should usually be one of your first troubleshooting steps.

Refer:

How to use the System File Checker tool to troubleshoot missing or corrupted system files on Windows Vista or on Windows 7
http://support.microsoft.com/kb/929833

Once SFC scan is done, try and install iTunes in administrator mode.

To install in administrator mode,

1. Locate the program icon, right-click click Run as administrator.

Hi Suuresh Kumar,

I have followed all of the things you explained above. Some of them I had done already but thought to give it another try. So far no result... I have download QuickTimes separate and installed it. It did install well but now iTunes wont start. I also downloaded audacity to see of that would install and work and that went fine. So  the trouble is only with iTunes.... I have uninstalled iTunes and QuickTime again and after reboot installed it again with the original download from iTunes.  When I wanted to start iTunes up it now comes with the following message:

Windows cannot access the specified device, path or file. You may not have the appropriate permission to access the item. Also when I try to open it as: run as administrator it will deny me acces..... This really is not funny anymore!!! I have tried to uninstall it but it won´t let me do that aswell.

Thank you for you help it is apriciated. I do hope you can help me some more!

Just another update.To get it all "working" again I went to a restore point and, of course, I had to install it all again. It still comes up with the same error, appart from that I can open iTunes now. When I did the restore point and connected the ipod it was reconized but iTunes would not open as it was missing files. After all the automatic updates where installed again the same problem occured. I went back with the restore point to the 12th of January. Thought you might want to know.

Hello m.kobessen,

You should remove all instances of iTunes and the rest of the components listed below:

it may be necessary to remove all traces of iTunes, QuickTime, and related software components from your computer before reinstalling iTunes. 

Use the Control Panel to uninstall iTunes and related software components in the following order:

1. iTunes
2. QuickTime
3. Apple Software Update
4. Apple Mobile Device Support
5. Bonjour 
6. Apple Application Support (iTunes 9 or later)

Follow the instructions from Apple article listed here: http://support.apple.com/kb/HT1923 to remove all components
Removing and reinstalling iTunes, QuickTime, and other software components for Windows Vista or Windows 7