I hope you have solved your problem by now.
But for those who have had similar problems recently, like the return key suddenly not working, I received a solution from Logitech.
1. Turn off all other devices besides the Bluetooth keyboard
2. Make sure the keyboard is charged
3. Turn the keyboard off and then back on
4. On your iPad/iPad mini, turn Bluetooth off and on
5. Turn your iPad/iPad mini off and then back on
6. Un-pair and then re-pair the keyboard with the iPad/iPad mini’s Bluetooth function
7. Reset Network settings (go to Settings > General > Reset , Tap Reset Network Settings)
8. Reset All setting: (go to Settings > General > Reset and tap Reset all settings)
My problem may or may not have been related to my recent upgrade to iOS 7.0.4.
I posted more about my experience at http://magree.blogspot.com/2014/02/to-get-good-service-be-persistent.html.
Apple and Logitech did it again.
After the upgrade to iOS 7.0.6 (never saw 7.0.5) the return key on my Logitech Solar KB Folio doesn't work.
I tried the steps above from Logitech and they did not work. I sent email to Logitech but haven't received a response yet.
The iOS 7.0.6 update also had the side effect of resetting my wallpaper to some standard setting. This did not happen with the update on my iPhone.
Persistence pays off!
I followed the instructions above precisely (it helped to see them on a MacBook Pro screen rather than on an iPhone screen.
The virtual keyboard kept appearing even when the Bluetooth icon was not dimmed. I typed something with the virtual keyboard and then I was able to make it disappear. Still nothing with the return key. After I pressed it many times did I see the cursor jump down the page.
Hey, Apple! Please test this before you release iOS 7.0.7!
It happened again with iOS 7.1!!! After much fussing about with a variety of forgottn steps, I have the return key working again.
I also added some of the suggestions given in https://discussions.apple.com/message/23242669#23242669.