I have the same problem this morning. my phone was totally fine and i charged it for like 15 minutes and suddenly it ask me to put my apple id and password but then it wont let me activated my phone. i press the home and lock button for like 10 seconds and when i turn it on, it still the same PLUS i have to connect to my wifi and suddenly it couldn't connected although i've put the correct password for m wifi (and I tried it in several wifi with password, the phone keep saying the password is invalid). Then later I used a wifi that has "public" purpose (which mean: no password wifi needed) and it can connected with my iphone 5s.
But still, it keep saying "your phone couldn't be activated. try again"
and I turn off my phone for like 2 time. and on my 2nd trial, it give me chance to put Apple id and password again. (please be carefull when typing it or it will going back to "your phone couldn't be activated." phase.
and my phone is back!!!! yay. hope my answer help anyone out there that having the same problem as me. cause today I surf everywhere there's no solution for this problem. I hope my answer could help you.