My Nikon D3100 is broken. I think?

All of the sudden, my camera won't take any pictures on any mode. Whenever I press the shutter release it just makes a really weird squeaking noise and won't focus on the subject. Do I have to take it in somewhere to be fixed?

"weird squeaking noise"; what happens when you try to focus manually? Put your lens and camera in manual focus and see if the focus ring turns easily. If it doesn't, borrow somebody's Nikon lens and try it. You may get to find out about the lens warranty. Work with Nikon Support on this.

In addition, if you are too close to the subject of very low light, the camera will continue to hunt and never quit trying. As mentioned, on the lens flip the switch to M and see if it will snap a shot then. If so, try letting it focus on something more distant and in better light.