5G video, Replaced new battery,still wont charge,here's what ive done

Question

My english isnt very well, hope u understand most of it. If you are impatient with my story you could just scroll down to the bottom,
Ok, so, my 60gb 5g ipod video is about 2yrs old. The drain battery thing starts happening a year ago.
With a full charge(as the screen said), once it's unplug from power source, it dies within 1 mins. so, i bought a new battery on ebay(hang on dont say the battery is bad, keep reading) put it in. That slightly improved, with makes it play for about 2hrs with a full charge. Not long after the replacement of this new battery, the ipod starts draining,and die quick again.
I decided to give it one more chance, and got a more expensive battery from ebay again.
after i replaced the battery, plug it into charge, it already says fully charged. At first i thought maybe it comes charged. so i unplug it. but the battery meter reads low, with like maybe 5% left.
That's when i realize, the problem is not the battery but the ipod.
I've read hundreds and hundreds of thread online. doesn't really help. I did all those reset
, disk mode and restore. The ipod still thinks the battery is charged and wont let juice pass on to the battery. At last, I've found a 13.1.2.1 firmware, and downgraded it from a 1.3, and see how it goes. Sadly, nothing changed.
@@@@@@@@@@   IF you are impatient, JUST read this part @@@@@@@@@@@@@@@@@
I took the NEW battery out, found a 3.7v charger, and charge it externally / manually.
put it back in, the battery meter( the one of right top corner, while unplug) reads a 80% charge)
so, this proves that the battery is 100% GOOD ! when i plug it in, the ipod still thinks the battery is charged and wont charge it.
Here's my conclusion. There's a problem with the motherboard/mainboard, either the chip that prohibits battery from over charging is out, or there is something wrong with the socket.
My solution(which I haven't done yet) is drill a hole on the back plate close the the battery location, Charge it from the outside, with wires directly connect to the battery(if u rip those plastic tape carefully, u would see the +/- connectors).
Cost: 3.7v charged, should be less than $15 or just find a unused cell phone charged.
       or just mod your ipod wall charged.
       Connectors between the wires to the battery and the external charger could be find it
      Wal-mart, Ace, and many other store. for Wal-Mart they are usually in the Auto  section. Should be around $5
So, the whole fix for mine is just $10, since i mod my own ipod charged. and the $5 tips at a auto shop for the guy that drill the hole for me.
This saves me $90 from buying a used 60gb ipod from ebay, and around $300-$400 from a new one at apple.
After all, I post this because i dislike the way apple treat their costumers, they simply wants you to buy a new one instead of helping you. I've read lots and lots of stories about how people are unhappy, upset and even angry with apple. I'm one of the millions.

Answer 1

by the way, replacing the motherboard cost about $55 if u do it yourself, which i would rather buy a new one if thats the case.
and sorry that i didnt do a proof reading, of which lots of error in my post.