I have configured the script and it works fine in Mozilla (Firefox/Netscape). When I open the page in Internet Explorer the script doesn't work.

Often this issue is caused by the configuration error that IE can't tolerate. Make sure there is no comma after the last elements of the lists in the configuration files. For example in Tigra Validator configuration following code will trigger the error in IE, while working fine in Mozilla browsers:

[... beginning of the structure is skipped...]
    'first_name':{'l':'First Name','r':true,'f':'alpha','t':'t_first_name'},
    'last_name':{'l':'Last Name','r':true,'f':'alpha','t':'t_last_name'}, // <- this comma
};

Similarly in Tigra Menu configuration following fragment will cause the problem in IE:

            ['Win32 Browsers', null, null,
                ['Internet Explorer 5+'],
                ['Netscape 6.0+'],
                ['Mozilla 0.9+'],
                ['AOL 5+'],
                ['Opera 5+'], // <-- because of this comma
            ],

Make sure to enable the error reporting in the browser to see more information. If the script's initialization code is present in the document then the script will either work or give the error message.