3 problems with my ipod touch

This is my first post here and I'm hoping someone will be able to help me out. A few days ago the screen froze on the apple logo. This happened to me about 9 months ago and I was able to fix this by restoring the factory settings. I can't seem to do this now because 1) when I plug it into my computer and try to connect to itunes, nothing comes up; it won't recognize it and 2) it will not charge at all (right before it froze; it was an almost dead battery). I left it plugged in the wall outlet and computer and will not charge.

After doing a lot of research the past few days and trying all these things people suggest to do, nothing works. I also saw that it could be a faulty USB cord? If that is true would I be able to use (borrow) someone else's USB cord (like for an iphone)? I don't want to waste money buying one if that's not really the problem.

Hoping I can get some ideas about how to fix these problems.

 

I don't know the exact model because I got it as a Christmas gift in 2009. So whatever the latest one was then, I guess. I got it from a friend of my mom's who got it for free with a purchase of a car- she didn't want it so she gave it to me. When I got it all I got were the ipod, usb cord, and earbuds.

I'm not sure what jailbroken means. Only in the past few days have I even seen that word from looking up stuff on how to fix it. I don't think it's jailbroken.

And no it has not been dropped or damaged by water.

 

I tried both DFU and recovery and neither work. I'm going to borrow a cable from someone, but it'll be a few days before I do that.

 

Before I get the cable I'll try the DFU and recovery modes again and see if it'll work this time.

 

see post #5

 

I looked at this page for a reference and I know I have an 8GB so it looks like I have a 2nd generation. According to that it's older than I thought (first introduced in 2008)

http://support.apple.com/kb/HT1353#iPod_touch_2nd_generation

Also, is there somewhere on the Apple site that I can type in my serial number and it'll tell me exactly when it was purchased and/or the model? I'm just curious....