If it is not a permissions problem, I would take a look at it with something like Process Monitor setting a filter for chrome, and when you get the error, see exactly what operation failed.
Then, if it is something like a specific access denied, or file not found, or something similar, you can do more specific troubleshooting/repairs.
This is most likely a problem with GoogleUpdate.
The simplest answer is to allow Chrome to log into google and save all your settings, including bookmarks and extensions and such. (In the settings screen you can tell it to connect)
Before you connect, use the button right below that to decide what you want backed up. You can exclude browsing and download histories and just keep bookmarks and extensions, or whatever you choose.
You can create a new google (gmail) account for just this one thing if you don't already have one..
Then give it some time to do the synchronization.
You can watch in task manager to see when the network traffic tapers off as it finishes.
After that, go into settings and tell it to disconnect.
Don't uninstall Chrome.
Download a new copy of Chrome from http://chrome.google.com
Close Chrome.
If task manager shows leftover chrome.exe processes, you can either reboot or open an administrator CMD window and issue the command
Taskkill /F /IM chrome.exe
Then run the new Chrome install file.
It will automatically reinstall the Updater software.
After it is up and running, go back to settings and tell it to connect to the Google account, and it will re-synchronize your settings, bookmarks, extensions, etc. - whatever you told it to synchronize in the first place.
After that you can decide whether or not you want to continue to allow it to keep you sync'd to Google or not.
You are free to disconnect and never use that Google account again if you wish.
One significant advantage of continuing to keep it connected is, if you have more than one computer, to allow that google account to keep your bookmarks and extensions synchronized across all of them. Including anything Android.
Best Answer
I downloaded the standalone installer for all users and it worked. Since it needs administrator privileges to install for all users, it's probable that the non-standalone, single-user installer didn't work because administrator privileges were not explicitly granted.