The Digital Rights Management (DRM) built into Windows Media Center encrypts recordings which are marked "copy once" by the content provider (cable company). These are considered "copy protected" and can only be played back by the same Windows system that did the recording in the first place. In fact, the recordings are in a WTV wrapper which is where that strict DRM mechanism gets implemented.
Anything marked "copy protected" in the WTV recording cannot be played back by any program other than WMC. You can't even use Windows Media Player on the same machine... you must use Windows Media Center. And you also cannot use either Windows Media Center or Windows Media Player on any other Windows machine to play "copy protected" content. Them's the rules.
In fact, the decryption key is time-based and also specific to the specific machine hardware and installed Windows configuration. If you make a radical change to your setup (including in particular reinstalling Windows from scratch on the identical hardware) all of your current "copy protected" WTV recordings will no longer be playable, even with Windows Media Center on that same machine. The decryption key is very very specific.
So, my speculation is that your recordings are from content being delivered from your provider marked as "copy once" and are thus producing WTV recordings declared as "copy protected", which means you can't play them on any other Windows machine but the one you did the recording on.
If you go into your list of "Recorded TV" programs, and you select any program to see its information and to push the play/resume/delete buttons, at the bottom of the window you will see "copy protected"... if "copy once" is how it got delivered and then recorded as "copy protected". You will never be able to play this program on any machine other than the one you recorded it on.