As you've discovered iTunes needs write access to files in order to update any information. iTunes has no automatic media update feature and will only make the changes you enter in the Get info. dialogs. If it can't write to the file however, it
appears to make the changes, only to re-read the original data next time it accesses the file.
To make sure Windows Media Player doesn't make any automated changes to your tags open WMP, go to *Library > Options* and in the section *Automatic media information updates for files* remove any ticks agaisnt the following:
Retrieve additional information from the Internet
Rename music files using rip music settings
Rearrange music in the rip music folder, using rip music settings
Maintain my star ratings as global ratings in files
When you add art or change other information in iTunes it will immeditately attempt to update the tag. WMP on the other hand tries to optimise performance by scheduling updates as a background process. This often means however that the WMP database can have the correct information & art, while this information is missing from the file. The WMP option *Library > Apply Information Changes* should force this update, but this should have been done on your old system before you moved the data.
Neither iTunes or WMP read the hidden artwork files that WMP produces when importing files - WMP produces them to provide the graphic folders in Windows Explorer but they serve no other function.
Since you are where you are, the following should help you work out which files still need artwork.
*How to find tracks without artwork*
To find all the tracks without artwork so that you can update them you can try
http://www.stum.de/itunes-find-tracks-without-artwork/ for Windows or
http://dougscripts.com/itunes/scripts/ss.php?sp=trackswithoutartwork for Macs. Use Google, Amazon, Discogs etc. to locate relevant images. Ideally these should be square, 320x320 pixels or above and borderless to give the best results in the various menus. If you have artwork for some tracks of an album, but not others, find the album in the main music folder, select a track with artwork, right-click (Option-Click for Macs) on the art & click copy, then select all the tracks of the album, use CTRL-I or Command-I to *Get Info* and then paste the image into the artwork box.
I say 320x320 because I believe (from using TouchCopy) that it's the size used in the iPod cache so if you're going to crop or resize you might as well work to that size. Otherwise 200x200 is probably good enough.
tt2