My system is Wxp home and I am the administrator but why cannot I download new version of Adobe Air?

I'm sorry you're running into installation issues with AIR.  Microsoft has just released a new utility that can help resolve installation problems.  Would you mind giving this a try and let us know how it works for you?  When running the Fix it, go through the uninstall process and try to remove Adobe AIR from your system.  Once finished, download the latest version of AIR and install again.

Microsoft Install and Uninstall Fix It

If you still encounter problems, we'll need to review the AIR installer log to better diagnose the issue.  Please post back with the log contents.  You can find instructions for finding these logs here:

AIR Installer Log Instructions