Your second attempt with <string>IP_Address=1.2.3.4</string> used the correct structure. Without knowing more about your setup, it is difficult to say what the exact problem is, but I suspect that it is a mismatch in the custom field name. If you configured the custom field as "IP Address", then the value would need to be <string>IP Address=1.2.3.4</string>. Also, I noticed that the request you specified included several semi-colons which should be omitted. Your request should be something like:
<?xml version="1.0" encoding="utf-8"?>
<soap12:Envelope xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:soap12="http://www.w3.org/2003/05/soap-envelope">
<soap12:Body>
<SetTicketCustomFields xmlns="http://www.smartertools.com/SmarterTrack/Services2/svcTickets.asmx">
<authUserName>__(username)__</authUserName>
<authPassword>__(password)__</authPassword>
<ticketNumber>__(ticket#)__</ticketNumber>
<customFieldValues>
<string>IP Address=1.2.3.4</string>
</customFieldValues>
</SetTicketCustomFields>
</soap12:Body>
</soap12:Envelope>
Andrew Barker
Software Developer
SmarterTools Inc.
www.smartertools.com