To make the long (many hours) story short – if you suffer from “this account isn’t being synced”/“sync disabled”/“sync is experiencing problems” syndrome on your Android device and miss important events due to the fact that calendar entries entered on the phone are not propagated to your Google account – there are two forum posts you may want to look at. This one is the first worth checking. You may need to use different combination of keys though. I needed Volume UP/HOME/PWR. YMMV. For me this method of course didn’t work. Meaning, it didn’t bring the proper syncing to the phone. Why should it?
So I lost even MORE precious HOURS trying to find the right answer. Found it eventually here.
[…] Settings > Data Usage > tap menu soft key > select “Auto sync data” from pop up menu. Now go back to settings> accounts and sync has been re-enabled. […]