If the problem is offline only, it means there is a security
problem online!
You should be able to modify Internet Explorer settings in
Tools/Internet Options/Security/  then Custom level
 by reading the new options and activate ActiveX (signed,
unsigned(?) etc).
Remember that these settings are true for online browsing.
Why don't you switch to Firefox as there will be no more
activeX problems, browser helper components installed by ill
intended people, less spyware...
and much less security problems. You will have to install
java, Macromedia plugins, the extension IEview just in case
and browsing online or offline should be fine.
You will eventually have to modify Httrack Set
options/BrowserID to
 Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.1)
Gecko/20020826 or a more modern one in a next release (?)