Hi,
According to your description, I suppose that Word 2010 was destroyed by the "Coveter PDF" program.
Have you only opened the Word by double clicking Word icon in desktop? I recommend you press Win+R and type "WinWord.exe /s" to start Word with safe mode.
If Word can start, the shortcut might be broken, you'd better re-create a new one and send to desktop.
If Word still can't open, please try to repair Office to test.
In additional, you can download the backup Word from this site:
https://products.office.com/en-us/download-back-up-restore-microsoft-office-products?legRedir=true&CorrelationId=e21f4e92-9af6-4f34-b50e-86926a68a99e
Hope it's helpful.
Regards,
George Zhao
TechNet Community Support