All you need to do is, using a USB device, transfer files from the old computer to the new one, placing it wherever the corresponding new location is.
That might've come across as simply restating what you've tried, so here's an example:
In Windows XP, the path to your Sims data (save files, etc) is C:\Documents and Settings\Username\My Documents\Electronic Arts\The Sims 3, correct? On Windows 7, it is C:\Users\Username\Documents\Electronic Arts\The Sims 3. Simply transfer the files from where they are to where they should be. For instance, a file located at C:\Documents and Settings\Username\My Documents\Electronic Arts\The Sims 3\Screenshots\screenshot.jpg should be transferred to C:\Users\Username\Documents\Electronic Arts\The Sims 3\Screenshots\screenshot.jpg.