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From the phone (internal memory)? What brand and class is your microSD?
Were these videos the free one's you get from Xperia lounge as part of your new phone because if they are then they will cease to work due to DRM protection
Thommo has a point,is that the case? Take out the microSD and check the name and if there is a number on it.
The microSD might be corrupted or some apps might be acting up.First,check how it is in safe mode:
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008
So it is a class 4 microSD.The problem might be the speed.Can you check with other microSDs ? (I suggest at least class 6).