iPod flashing apple when plugged in to computer?

hi,

I bought my 120gb ipod classic of off a friend, it worked for 5 hours then stopped working, it had 3/4 of a battery when i checked it like 5 mins before it quit working. it said to plug in to itunes to restore. I tried plugging it in to itunes but itunes and my computer would not read it. It had a permently black screen when not unplugged, and when you plugged it in it flashed the apple logo. I replaced the battery thinking that this would fix it. after replacing the bettery, i let it charge overnight. this morning i checked it and it had a faint apple, noww it is back to the blinking apple. This thing has got me so mad it is not funny. The people at geeksquad told me that it might be some kind of software problem and to send it to apple but im a single mom and i cant aford that at all. thanks in advance for any help i need to save this thing.

P.s. I have made sure the hold button is not on, i have tryed the toggle hold,press menu&center, the computer will make the noise that sounds like it reconized it but it will not show up in computer or itunes. when it is plugged in and i hold the center and top button however itunes will load and say it is perpairng for recovery, that will load fully and then it goes back to the traditional itunes screan without reconizing it, someitmes i will get either the 2005 error or the 1621 error saying it is discovered but not reconized?