Cannot connect Apple Server to restore my iPhone from iCloud after upgrading to iOS8!! Why?

The only other suggestion would be to unplug your wifi router for 15 seconds and plug it back in, then go to Settings>General>Reset, tap Reset Network Settings, then go to Settings>wifi and rejoin you network. Then try restoring the backup again. (Note: resetting network settings erases passwords for previously joined networks.)

FYI, this is Apple's description of the error message it sounds like you are getting:

The link in this screenshot is here: If you need help restoring an iCloud backup. (It's the same article, it's just been renamed.)

You don't restore an iCloud backup using your Mac or usb cable. You have to restore it using wifi on the phone itself. This explains how to restore and iCloud backup: iCloud: Restore your iOS device from iCloud.

You're welcome. Disconnect your phone from your computer and confirm that you are connected to wifi, then try going to https://appleid.apple.com/ using Safari on your phone (or just search for My Apple ID, then click the link to Apple - My Apple ID). That will confirm that you are able to connect to a secure website over the internet using wifi. Are you able to launch this webpage on your phone?

I see. I wonder if you might have a weak or intermittent wifi connection. You might try moving the phone closer to your wifi router and trying again. If that doesn't help, it also could be just a glitch caused by Apple's servers being overloaded with people trying to restore an iCloud backup right now after updating to iOS 8 or purchasing the new iPhone 6. If that's what's causing it you might want to wait a while and try later, or if it's late where you are, try again tomorrow.

What error message are you getting?

I have to run now but see if that works for you. If not, we can pick this up again tomorrow.