Flash PIT - this will fix it
You need to flash the PIT with ODIN, latest version (3.09, I believe). Google for a download mirror that hosts the PIT for whichever type of note 3 you have, then flash it with odin (should work while in the invalid software screen). Then, if it doesn't reboot, just remove the battery and unplug that sucka. When it reboots, it should go back to download mode or just regular bootup. I recommend setting up adb, which makes it much easier to put the phone into whatever mode you desire with a simple dos command.