So it never says that it's "connected"? Are you certain that the password you're entering is correct (if you have one)?
And have you tried resetting your router, as well as pulling the battery out of your phone? There is an actual difference in pulling out the battery and just turning it off and on through the software. If you've already done that though, I would try downloading a 3rd party WiFi manager app from the Play store and see if that works.
If that still doesn't, a factory reset may be inevitable to fix the situation. I've worked at several cell phone companies dealing with smartphones and I can't tell you how many times I've had to do a factory reset to fix something (usually as a last resort).
Smartphones can just be fickle sometimes...