Automatic backups from Onenote?

I have to admit that I am running out of ideas.

You could try doing a repair (I know it says Access, but it covers all Office programs):
Repair or remove Office 2010 - Access - Microsoft Office
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Repair your Office 2010 programs

Repair your Office 2010 programs by doing the following:

1. Click Start, then click Control Panel.
2. Click Programs and Features.
3. Click the Office 2010 program that you want to repair, then click Change.
4. Click Repair, then click Continue. You might need to restart your computer after the repair is complete.

Perhaps if you modify the save locations back to their original state?

The following illustration shows my OneNote save paths which have not been changed at all - naturally, you will need to change the "Irene's Win7" to whatever your own was.
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In your original post, you were looking for a free online storage facility - I have not used it myself, but what about Skydrive?:
Skydrive - Windows Live - 25 GB Free Storage