So if you reboot your iPhone (not shut down and turn on, but reboot, like thee reboot command from NCSettings), while not plugged in, it works fine? Because from what I've seen, a tremendous amount of people have this issue, and it isn't from installing packages. The good news is that it's an annoyance, as being plugged in to a power source allows a reboot, as does booting to safe mode, then shutting down and turning back on, but this is a bug somewhere in the code. Seems to only affect iPhones, however.
Oh, and I did the exact same thing you did to jailbreak my 5.