Bottom slider doesn't work...among other things

I've had my iPad 3G 32GB for about 60 days or so. Just recently, I've been experiencing problem with my device. The home slider that reads (slide to unlock) is not working and seems to be stuck. It won't move as I slide the button to the right (IT'S STUCK). But once I rotate the iPad to access the other slider options, they work fine.

Another problem I ran into is as I'm using the iPad it would start to freak out! Like it was possessed or something. If I was using an app, it would shut the app off or pull up the keyboard (if the app used one) and caps lock button would go off and on, keys would start being pressed...you get the picture. I've tried numerous hard restarts, restoring it, wiping the whole ipad, wiping all my apps, taking out the microSIM and restarting. I'm running out of options.

Bad enough I live on Guam which has no Apple Store or support. I had ask my dad to pick one up for me while he was in Washington state. Any help would be much appreciate.