All - Seriously need to pass this on to all Nokia Lumia users. I have the Lumia Icon and was having the exact same issue with the power button and Wi-Fi connectivity thing. Nokia/Verizon recently put out a firmware update to correct the Wi-Fi issue, but it wasn't pushed out for WP8.1 users; so, no fix for WP8.1 users. This is what I did.
1. Back up EVERYTHING you don't want to lose from your phone to your PC! BACKUP BACKUP BACKUP!
2. Download the Nokia Software Recovery Tool from Nokia's website.
3. Install the software on your PC.
4. Connect your phone to your PC and run the NSRT. DO NOT DISCONNECT THE PHONE UNTIL THIS HAS COMPLETED FULLY! NSRT will download the latest firmware and software for your phone. For Lumia Icon users this will INCLUDE the latest Wi-Fi firmware upgrade fix. This is a VERY LONG process. The file is 4.29 GB (for Icon) and you should use a high-speed internet connection (the faster the better).
5. Once FULLY completed, if you are not going to upgrade to WP8.1 DP again, go ahead and reinstall your apps and enjoy WP8.0 until the final release comes from Verizon. If you ARE going to re-upgrade to WP8.1 DP, HOLD OFF on reinstalling your apps. The reason is that some of the previous apps for WP8.0 are not designed for 8.1 and might be causing issues if already installed prior to upgrading. These apps will be known once you upgrade. They will be listed as "incompatible" in the app store.
6. FOR THOSE UPGRADING TO 8.1 - Go ahead and download and install the Preview for Developers App in the store and run it.
7. Upgrade to WP8.1 DP as you did before.
8. Once upgraded, DO NOT use the Restore from Backup feature!!! MANUALLY install apps from the App Store (using "my apps" section). Recommend you do this over Wi-Fi so you don't eat up your cellular data plan. This is where you will see the apps that aren't suggested to be "compatible" with WP8.1.
I did this and my Lumia Icon is working just like it did with WP8.0. No lag, no power button issue, no Wi-Fi issue. No battery drain! No problems whatsoever! If this doesn't work for you, I'm sorry, but it worked for me and I just want to pass it on in case it helps others! Thanks!