Just to clarify - you're talking about returning the details of the users own computer right?
In this case if your code is running on the server as a web part then the only thing you're going to be able to provide is the IP address - nothing else is available remotely.
Think about the security implications if this were so - no need for cookies, every website on earth would know your MAC address (totally unique), computer name, company domain etc etc.
If you really need this (and I can't for the life of me imagine the use case for this above a "You last logged on at such a time from ip xxx") then you need to have a program running on the client (users) side - ActiveX/Java/Silverlight - but I would expect they are also restricted (esp Java/Silverlight) in getting this sort of info.