Are there config settings in Kaspersky that allow it to "Ignore" certain files and folders? If so, set it to ignore the OE identity files.
Try a system restore to a date prior to the Kaspersky update.
If no joy, disconnect your PC from the network, then uninstall Kaspersky and see if you can run Outlook Express Backup Wizard.
If so, then re-install Kaspersky and try again.
Alternatively, uninstall and re-install Outlook Express Backup Wizard.
If that still doesn't work, you can manually back up all your email (from the OE identity mentioned above), then remove OE and start over, in case it's OE that has been corrupted. Import all your messages back, either manually, or using OEBW.
There's another recent thread with advice / warnings about OE and size of inbox / sent items - check you aren't approaching a hard limit.
Finally, OE is so easy to back up manually, I would hesitate to pay for a backup solution. But then I am a tight dastard!
SD