I reasoned my way into a solution. My thinking was:The Device Manager says both DVD drives are working correctly and both are new and one is Sony and the other ASUS so I think a problem with the drives unlikely. The problem is with Windows Media Center not "DETECTING the DVD". So there must be a problem with Windows Media Center. I thought I might need to reinstall Windows 7... then I thought maybe if I just reinstall Windows Media that will work. It did. My Fix was:
start>control panel>Programs and features>Turn Windows features on or off> then uncheck the box for Media Features>reboot computer>then recheck the box to restore Media Features> Now both drives play both DVDs I had been trying. Both drives work normally. Reinstalling the Media Features of Windows 7 fixed the problem. Thanks to all who offered solutions.