Raspberry Pi WiFi ONLY works if Ethernet is plugged

I have a headless Raspberry PI model B, with a RealTek 802.11n dongle, running the very latest version of Raspbian.

I would like to configure both the wired and wireless connections so that I can choose to plugin to the Ethernet if need be. However, most of the time I would like to connect via wireless. The wireless network utilizes WPA2 Personal with a hidden SSID.

    If I boot with both the Ethernet and Wifi plugged in, the network connectivity will work over both Ethernet
    and WiFi.
    If I boot without the Ethernet, I can not connect to the Pi via WiFi.
    About 15-30 seconds after plugging in the Ethernet, both Ethernet and WiFi network connectivity will work.
    If I unplug the Ethernet, I can no longer connect to the Pi via WiFi.

Below is my /etc/network/interfaces file. What changes do I need to make so I can use the Wireless connection without the wire?