I would look at your NAS first, before worrying about AV software, if playback used to work fine.
The problem happened on both PCs, and the NAS is a common element to both the old and new setup. I assume that you have the same AV software on the new PC as the old had, so that could still be a problem. In fact, if a NAS is a bit slow in delivering files, and then AV software analyses every file delivered, it can be the combination of both that causes stuttering of music.
But first the NAS:
Do you have utilities that can check the health of your NAS?
Are all the disks on the NAS in good condition?
Is it getting full, or old?
Is it running the latest firmware?
Had you made any changes to the NAS around the time the problem started?
Perhaps create a new, empty library on the new PC, copy a few files across from the NAS to the local hard disk on that PC, and then import them into the local library. Then see if the playback problem happens with those files. Be careful when using multiple libraries and switching between them that you are on the correct library when you do maintenance. You don't want to damage you main library!
Read these if you aren't familiar with using multiple libraries.
http://wiki.jriver.com/index.php/Libraryhttp://wiki.jriver.com/index.php/Library_Manager