I've come up with a solution using AutoHotkey. Compile the script and then run the executable. Your IP address will be quickly copied to the clipboard! This takes the first address from the the output of ipconfig /all. If you need help customizing the script, just let me know. :)
Download:
http://ahk.igalvez.net/GetIPv4.exe, 784 KB, Windows 7
Clipboard =myCommand = ipconfig /all | find "IPv4" | clipRun cmd.exeSend %myCommand%{Enter}Sleep, 500Send exit{Enter}myString = %Clipboard%StringReplace, myString, myString, %A_Space%, , AllStringReplace, myString, myString, IPv4Address...........:, , AllStringReplace, myString, myString, (Preferred), , AllStringSplit, myLines, myString, `r`nClipboard = %myLines1%ExitApp