Content will go to the app that you tell it to go to, it doesn't happen automatically. If you synced them through your computer's iTunes (i.e. via the Music tab in iTunes) then they should be in the Music app (and similarly for videos to the Videos app). If you want them in the Media Player Classic app then you might be able to transfer them to it via the file sharing section at the bottom of the iPad device's apps tab when connected to iTunes or via your wifi network (I don't know what that app supports, and the link to the developer's website doesn't appear to work)
Syncing music to the Music app : http://support.apple.com/kb/HT1351
iTunes on the iPad is just the iTunes store, your synced videos and TV shows will go into the iPad's Videos app, and music and audiobooks into the Music app. My post was referring to iTunes on your computer, and how to use it to sync content to the iPad.
You can enable a left-hand sidbar on your computer's iTunes via control-S on a PC, which may make the following easier to follow. Connect the iPad to your computer and select it on that left-hand sidebar of your computer's iTunes, and then on the right-hand side there should be a series of tabs, one of which should be Movies - if you select that tab you can then select which of the videos that you have on your computer's iTunes that you want to sync to the iPad's Videos app.