I think you might be confusing "downloading" with "installing". Downloading is the process of copying the file from Just Trains to your computer over the Internet. As you have it on your desktop, that process seems to have started. However, it might not have completed. Right click the icon and check the file size.
Installing is the process of running the downloaded file on your computer so it extracts its contents and updates your copy of Trainz. It seems to be that process which is stalling at 0%.
The first number in the filename of the SP1 file you downloaded must agree precisely with your current build number. Can you check it does please.
Before installing SP1 you must uninstall and reinstall TRS2006 but not run it, not even once. Refer to the installation instructions for SP1 and be sure to follow them to the letter. The slightest deviation will cause the update to fail.
Sorry if I've misunderstood what's going on. BTW, you're not alone, a lot of people find installing SP1 a pain.
John