I'd start off by saying, "First of all, jailbreaking your iPhone is a bad idea...", but I've jailbroken my iPhone in the past and decided that the approximate 70% of normal battery life was just unacceptable, so I restored it.
Anyways, it sounds like your device might be stuck trying to boot up and that's preventing iTunes from connecting properly.
I would suggest putting your iOS device into Recovery mode by:
Connecting your device to your computer with iTunes open.
Press and hold the Home button and the Lock button at the same time.
As soon as the screen turns completely black, release the Lock button. Continue holding the Home button until iTunes pops up a message saying that it detected a device in Recovery mode.
From here you should be able to restore your device.
Your device's screen should indicate that you should connect it to iTunes. It'll have the iTunes logo and the iOS device end of the connection cable on it.
If that doesn't work than I would suggest trying the same process, but with DFU mode.
The only difference is that instead of releasing the Lock button when the screen turns black, release it after 10 seconds from when you first pressed it.
This time your device's screen will remain black.
DFU mode may take a few tries, just keep trying until you've done it and there's nothing on your screen.
Let me know which method worked for you. (Unless neither worked of course.)