iPod touch iPod touch will not restore properly (SOLVED!)

This is going to be a long story, but fortunately I do have a very specific problem, and I am hoping someone on this forum may be able to help me.

I have an 8gb 1st generation ipod touch. It works fine, I can use the screen and the apps and play music and connect with wi-fi no problem. However, the iPod would not recognize a computer connection. That is, when I would plug it into the computer via USB, the ipod would just remain in its normal state, as though it had not even been plugged in. The computer wouldn't recognize it, and neither would iTunes.

I tried everything, reinstalling itunes, using a different computer, restarting the computer, updating to the latest version of itunes, testing different usb ports and cables, and so on. I finally decided, in a desperate attempt, to completely restore the iPod, as I wasn't sure this failure to sync to communicate with the computer was a symptom of jailbreaking or not. While I have not jailbroken the computer, it is possible the prior owner who sold it to me did.

In any event, I completely deleted all settings for the iPod, by using its built-in settings menu. I ran a full restore, and it seemed to work properly. The iPod touch reverted to the iTunes and cable screen, so I plugged it in. Still no response. Now the iPod is locked up on the screen. I can turn the iPod off and restart it, but it just continues to revert back to that screen, and the computer and itunes will still not recognize it. I don't even hear any sound from the computer confirming that it has connected. I've tested in on three different computers and got the same result. I've tried to do a soft and hard reset, but nothing has worked so far. Is there anything that I can do to fix this outrageous error, or am I forced to turn it to Apple for an overhaul or replacement?

Please let me know if there is a solution available. I have searched exhaustively through the internet for a solution, but I have found none. Thank you for taking the time to read my post.

Forgive me for my ignorance, but what is DFU mode? Maybe that could help the computer recognize the iPod.

Also, I noticed that the screen the device is stuck on can't be recovery mode, because while there is a connect to Itunes screen, there is a small battery icon in the upper right hand corner. I thought that recovery mode just showed the USB cable and iTunes logo, and nothing else. If it also shows a battery, does that mean the iPod is technically in regular mode, waiting to be connected, or something else?

Well, I have taken the iPod in for repairs, as DFU mode did not work. It appears the iPod has a bad logic board, and the price to replace that particular part is not worth the cost of simply getting a new iPod, so that is what I think I will do. Thank you for your suggestions liamkp, it was worth the shot at least.