I had a similar error and it turned out to be a corruption of the NTFS permissions in %LOCALAPPDATA%\Microsoft\Internet Explorer. There are several possible system corruptions that can cause this problem, and they are well covered at a Stack Overflow answer about localStorage objects.
Coming from Excel, this is probably a corruption may be an incorrect integrity level in %userprofile%\Appdata\LocalLow, which affects the DOMStore at %userprofile%\Appdata\LocalLow\Microsoft Internet Explorer, where the DOMStore (localStorage) lives.
There is also a possible registry corruption issues, covered at https://stackoverflow.com/questions/13102116/access-denied-for-localstorage-in-ie10/23583134#23583134