It sounds like your Cube may have an older version of the software and perhaps that is causing some WiFi issues.
You can try our new-ish CubeDoctor application to bring your Cube completely up to date. The process is in beta, so any feedback is much appreciated.
First unzip the files below into a folder and then just connect your cube via USB cable to your PC or MAC, launch the program and click "Fix my Cube".
Let me know how it works for you to bring your Cube back to the most up-to-date factory condition, and then please try the Photon connection process again via the Particle App.
-Shawn, Looking Glass