This is a simple demo which works with the www.ipchicken.com site.

It sometimes chokes as it is looking for an HTML "BOLD" command - if this isn't present on the page it returns an incorrect value.

You can use this with a bit of error checking, or if you can find a site which uses named objects on the page you should be able to get a cleaner result.

Code:
$=SetOption("WrapAtEOL","ON")
$=SetOption("ASCII","ON")
 
$oIE = CreateObject("internetexplorer.application")
$oIE.Visible = 0
$oIE.Navigate("www.ipchicken.com")
While $oIE.busy AND $oIE.readystate <> 4 AND @ERROR = 0 Loop
$oDoc=$oIE.document
$sHTML=$oDoc.body.innerHTML
$oIE.Quit()
$oIE = 0
 
; Strip out IP address.
$sIP=SubStr($sHTML,InStr($sHTML,'<B>')+3)
$sIP=Left($sIP,InStr($sIP,' ')-1)
$sIP ?