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If you never made a backup of the template and stored it somewhere safe like in Notepad or some other plain text editor, you can reload (select again) one of Blogger's standard templates. It will merely overwrite the one that's gotten damaged. It will not damage your posts.
If you have customizations (such as links, etc. in the sidebar) in your current template, copy all that so that later you can Copy just those bits and Paste it into the new template to bring it up to par with how it was supposed to be.
If this works out, then you can make a new Safety Copy of the template! You know, right-click your mouse, then Select All, then right click again, and Copy. Keep it in memory and go straight to where you're placing the copy so that you can Paste it in there and save that file. Call it SafetyTemplate.txt or anything else you won't forget!
Attach date to filename:
Later you may want to keep several copies at a time, so you can attach a number or the date of the save to the file. Name it something you can remember.
Today is 09/04/06.
A saved template file might therefore be SafetyTemplate090406.txt
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The new system lets you download copies of the template to your hard disk, but since it's XML instead of HTML, you can't do as much with it. You can keep it safe, you can keep copies from different days. The Widgets are not there; they are evidently stored on the servers along with the posts. It's a different situation now.