It sounds to me as if the copy protection method on these CDs with "player" on them means that the only way to get a PC or laptop to play the music is to use the proprietary player included on the CD (the aforementioned player). this makes it very difficult to rip the cd using Musicmatch itunes etc etc. You could try ripping the files using isobuster, and then lame to encode. If this doesnt work, what I do is install total recorder, and use the proprietary player to play the songs, whilst recording them with total recorder. You can encode as MP3s and tag them with total recorder as well. Total recorder is not free, but it has allowed me to rip many of my cds that have copy protection.
When I first encounetred copy protection I was so annoyed about it, as I only rip cds that I have paid for, that once I had broken the copy protected cd I posted the ripped mp3s to a p2p network, just to get back at the record companies
thankfully the record companies are finally starting to address the different ways that people want to buy and listen to music. Thanks to Ipod for that one.
Total Recorder
LAME
Isobuster