Something appears to be wrong on Apple's end, server issues, making changes or something. I too have a perfectly fine internet connection (obviously), my AppleID is correct, I can view apps in the store but when I click "Install App" it processes for awhile then fails, saying "We can not complete your iTunes store request"
I am going to give you a bunch of basic troubleshooting steps that you can try.
1. Quit the app store completely and restart the iPad. Go to the home screen first by tapping the home button. Double tap the home button and the task bar will appear with all of your recent/open apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus sign in the upper left corner of the app that you want to close. Tap the home button or anywhere above the task bar. Restart the iPad.
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
2. Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
3. If that doesn't work - sign out of your account, restart the iPad and then sign in again.
Settings>iTunes & App Store>Apple ID. Tap your ID and sign out. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Go back to Settings>iTunes & App Store>Sign in and then try to download again.
4. You can try resetting all settings. Settings>General>Reset>Reset All Settings. You will have to enter all of your device settings again.... All of the settings in the settings app will have to be re-entered.The new iPad, iOS 6, 64GB WiFi