No. I tried going to support.microsoft.com, who said to download/install Windows Easy Transfer on both PCs, the old one with Windows XP, and the new one with Windows 7. The new PC (Windows & has W.E.T. already installed, but this one, the old one (Windows XP Hpme, does not, so I went to this PCs' Programs: Accessories/System Tools/Files transfers, but still could not get it o work.
You're using the wrong program.
Windows XP Home does not have Windows Easy Transfer, so you went somewhere on the Microsoft site and downloaded something. You should have gone to the web page linked above, where you would have had 4 choices: XP 32-bit, XP 64-bit, Vista 32-bit, and Vista 64-bit. Did you download the correct version for your system (almost certainly XP 32-bit)?
Assuming that you downloaded the correct version for your system, you should have then double-clicked the icon named "wet7xp_x86.exe" to install Windows Easy Transfer for Windows 7. The start icon for this should be at the bottom of your Start > All Programs list. It is NOT the same as the program that starts from Start > All Programs > Accessories > System Tools > Files and Settings Transfer Wizard. That is the old version, which was intended to transfer files, etc. from earlier versions of Windows TO Windows XP.