iCloud Verification failed

Hi everyone! I'm having trouble using iCloud in my iPhone 5S. I don't know why the setting changed but now I need to put my password again because iCloud is kind of offline. When I do, it says "Verification error. There's been a connection problem with iCloud" and won't verify. Hence, I can't sync my data.

I must say that the password is correct since I can log into iCloud on my Mac and web. Also, a complete reset + restore is impossible since I have the "Find my iPhone" ON and I need iCloud to disable it. Kind of beats the point...

Does anyone have a similar problem + solution?

Thanks.