I'm also having the same problem with the Videos app - interestingly enough, also with a 64GB 3rd Gen. Touch running 4.2.1 (build 8C148). Try to open Video app, it goes to white screen for a bit, then quits.
Checked out another thread (
http://discussions.apple.com/thread.jspa?messageID=12678404�) and experienced the same behaviors as well: temporarily works if you change languages; restoring as a new iPod does NOT fix issue; music videos seem to play fine (though it seems to repeat a video, rather than move on to the next); and all that.
The more I read about it, the more this seems to be a glitch in iOS. Moreover, it seems to be related to music videos somehow. Seems that the Music Videos and regular moves aren't playing nice.
While music videos do play in the Music app, that's not particularly convenient for me. Going off one of the posts in the above-mentioned thread, I'm going to tray a temporary fix of relabeling my "Music Videos" to "Movies". Seemed things went wrong when Music Videos entered the picture. While a work-around, for me it's a little more usable than the inverse.
Will report back whether or not this temporary fix works until Apple can release an update addressing this problem.