The same thing happened to me months ago. The thing is - you won't be able to apply to jobs unless you provide a valid ID. Here's why I didn't understand your post: how come you don't have an ID?
You must have National ID or Passport, everyone in the world has it. Of course that the student ID or library ID card is not valid. You must have an ID issued by government institutions in your country.
I hope you'll get it. In my case, I've provided my passport details and soon I was able to apply to jobs and work on oDesk normally.
No, not everyone in the world has a national ID or passport. Some countries don't issue national ID cards. Some people have no need to travel outside their country, so don't need passports.