Has your office installation also disappeared? When you double click on these OneNote files, are they unidentifiable ?

Go through these steps & it 'SHOULD' fix your problem.

1) Check to see if Office exists on your machine.
-If you're certain OneNote is not on there (but the others are) - reinstall office
-If you're certain office isn't on there at all - simply install office.
-If you find OneNote, proceed to step 2

2) Put all your OneNotes into one folder anywhere locatable.

3) Right click the unidentifiable OneNote workbook (any one) and click 'Open With'

4) You should see OneNote in a list here, click it so it's highlighted & then tick the 'Always use the selected program to open this kind of file'
-If you cannot see it, click 'Browse'
-You should be able to find by default links to your MSOffice installation in the startup, for windows 7 (your new machine) travel to:
"C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Microsoft Office"

If one note is there, select it as normal and keep the 'Always use the selected program to open this kind of file' box ticked! Simply click OK & try to re-open the workbook.