The simple fix to this is to include the script tag with the link to http://www.google-analytics.com/urchin.js at the bottom of webpage, which Google now recommends doing. If the Google Analytics website goes down, and the file is unavailable, the page will continue to display normally.
Although this solves the big problem of no content being display, there are still two issues.
The first is that any calls to the Google Analytics functions such as urchinTracker to track downloads or outbound links in click events will break. The script containing the function hasn't been loaded, either because Google is down or the user simply clicked the link before the page reached loading the script tag linking to Google. The solution to this is test whether the function exists before it is called.
<a href="webdialog/webdialog.msi" class="imagelink" onclick="if (typeof(urchinTracker) != 'undefined') urchinTracker('/downloads/webdialog');">
Google Analytics is a powerful service, at the right price (free!). Hopefully by taking these precautions you should be able to continue tracking visiters with Google Analytics without it interfering with the rest of your website.
What NOT to do!
Don't host a local copy of urchin.js yourself and link to that.
The reason Google is giving out a link to a file, rather than the file itself, is so that they can easily update it when fixing bugs or adding functionality. Updates will trickle down to all websites automatically.
If you are hosting urchin.js yourself then one day stats for your website may stop working without warning because your version of the file has become out of date.
Google has added a page about to their website about hosting the urchin.js file locally. For the same reasons I wrote above they don't recommend it.