A Few Different Problems on my iPad

I have 2 issues that have come up in the past few weeks and I have no idea how to fix them.

1. My screen won't rotate anymore. It is stuck in the portrait mode. I know that the rotation lock is not switched on. I have tried to do a wipe and restore from iCloud and the problem went away for a little while before coming back again.

2. I go to turn on my iPad by hitting the home button and nothing happens. Then I hit the sleep/wake button and still nothing happens. The only way that I can get the iPad to respond is to hold both buttons down for about 10 seconds to reboot my iPad. This is happening almost daily now.

And of course my iPad just went off of warranty. Any help would be much appreciated.

Thanks!