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Sorry to say but the only way to make sure this is not a hardware issue would be to load the apple software back on the phone to update the firmware and baseline, To do this can you press and hold down the power and the menu buttons for a full 15 seconds, during that time the phone should power up then shut down then power up then shut down again.
After it has shut down the second time can you open iTunes then connect your phone to the machine and see if it prompts you to recover the phone.
If it does it should then load the latest iPhone software to the unit so you can then see if it will work correctly.
If it does then you will need to have the phone re jailbroken to apply the latest jailbreak and reload your content.
Let me know if you need more info.
Did you hold down the power and home buttons so that it shut down, powered up and shut down a second time?
If so can you do the same thing to power it off then open itunes on your machine then press and continue to hold the home button down and connect the iPhone to your machine with the home button held down and tell me if it is seen by iTunes
Can you tell me if you had it jailbroken locally or did it yourself?
Legally I cannot give you instructions on how to help you hack or jailbrake your phone, however I can suggest that you may wish to use your tool to see if you can use it to read and reload the phone
In that case the only thing I can suggest is to try is a reload of iTunes, to do this can you open your My documents folder then open Music and open the iTunes folder.
From there can you right click on the iTunes music folder and choose copy then close the window and right click on an empty part of your desktop and choose Paste so that we have a copy of your iTunes library on the desktop.
Once that is done can you click Start then control panel and open Programs, Find iTunes in the list and give it a single click to highlight it then choose remove.
Once it is removed can you restart your computer then follow this link http://apple.com/itunes/download to download a fresh copy of iTunes to your desktop.
Once the program is downloaded can you install iTunes just like normal.
After it is finished can you then open iTunes and let me know if it will run properly and that all your music is listed.
If it is can you try connecting the phone once more andd seeing if it is seen by iTunes
So when you plug the phone in does iTunes show the phone on the left hand side?
As your phone is not being seen by iTunes either in normal mode or recovery mode there is not a lot more we can do.
I am sorry to say but the phone is bricked and all you can do would bbe to take it to the Apple store and see if they can get it to unlock so you can reload it.
Even if they give you a hard time about it being jailbroken,they will at least have to unlock it so they can run a diagnostic and find out it is jailbroken.
Let me know if you need more info
To run the diagnostic they will have to get it unlocked using specialized Apple software which they have available.