IPod Touch 1st Gen 1013 Restore Error Code

Question

So I have my iPod touch that I treat with the utmost care and it got stuck in the apple logo on startup. I tried restoring in the iTunes(hold home button and plug in USB) and DFU mode and I always get the 1013 error code. So yesterday I brought it into the Apple Store and they attempted to restore it and it gave them the 1013 error code. He told me that it was a generic error code and it would cost $250 to get a new 3rd Gen iPod Touch, which isn't a very ideal result. So I spent some time thinking about this and I thought why is it my problem that Apple can't fix their iPod especially if it's a generic error code. I take great care of my iPod and have nothing wrong so why should I be paying $250 for a new one? So today I called Apple Care support and after complaining to them they told me that the $250 would be the cost to *JUST REFURBRISH IT!* So I said "so if I am going to pay $250 dollars then shouldn't I just buy a new 32GB 3rd Gen iPod Touch?" The man said he agreed with me and that he was sorry there was nothing else he could do. I then asked if there was a way to see if the iPod had a software or hardware error and he asked if the genius at the store had run a diagnostics test. I said no because all I had was a restore done and I was sent on my way. He said that the store should have run a diagnostics test because it was protocol. So now I have to go back into the Apple Store and get a diagnostics test run on my iPod because the initial genius didn't follow protocol and just insisted that the iPod touch had a hardware failure so it was out of warranty. I highly doubted it was a hardware failure because restoring the firmware is a software issue. And nobody can give me solid facts why it's not, other than the genius thinking he really is a "genius" and telling me it's not because he didn't follow protocol.
So tell me what else you think I should do other than get the diagnostics test run. Any comments or input would be much appreciated.
My overall goal would be to have my iPod replace or fixed for free because that would be the reasonable thing to do. Especially because all the trouble Apple has cause me thus far.

Answer 1

as directed by referenced guide followed steps below
recovery mode method
connect ipod device shows usb i tunes screen
dectected by itunes as ipod in recovery mode must restore to use
select restore/update to factory settings
Extracting then preparing ipod to restore
powers off after white screen flash disconect sound is heard, powers on black screen with apple connect sound heard, powers off to black screen diconect sound heard
error 1603 could not restore
DUF mode method
same as before except black screen due to duf mode
error 1604 (not 1603)
Manual Install method
Downloaded appropriate files
connected device itunes recognizes as in recovery mode
selected software with the shift+restore method
preparing to restore
white screen disconect connect black screen with apple logo then dicnnect black screen
could not restore error 1603
any other recomendations?