Check and make sure no jumpers on the logic board aren't broken or missing. Try a soft reset, then a hard reset. Make sure the display connections are fully connected. Reseat them if you have to. Make sure the pins on the display connections on the logic board aren't bent or broken.
Something similar happened to me but I later found out that the phone was exposed to liquid (albeit briefly). Another instance was I somehow broke off a microscopic piece on the logic board. Get a really strong magnifier and look at the logic board to make sure no jumpers,etc.have broken off. If you see something missing/damaged, it'll need to be microsoldered back on. Also look at the digitizer connection on the logic board to make sure any of the pins haven't been bent or broken. Age of the phone doesn't necessarily doom the phone, just the condition of it. Good luck and I hope I helped.
This happened to me with a different version of iPhone. Long story short what happened is that I somehow broke off a very tiny jumper right next to where the battery connects to the logic board. If you have a magnifier with light, open the phone and inspect the logic board very carefully for broken/missing jumpers. You won't be able to see anything without the magnifier. If that's the case, you'll need to micro-solder to fix it. Sorry, this is more likely the problem if a battery change doesn't fix the charging issue. Hope this helps.
are you getting an error message? is safari locking up? what exactly is happening, even if you say "i tap the icon and nothing happens"? if you go to a bookmark or a link on an email, does it still open safari or no? I need more information. sorry and thanks.
The antenna is on the top left hand side of the phone and partially stuck onto the screen. You can easily damage it if you are not careful. It could also be disconnected from the logic board. make sure it's attached to the underside of the logic board. if it still says no service, then replace it. it's a pretty cheap part, only about a couple of bucks. Last resort, logic board could also be damaged (uh oh), but I say try replacing the antenna first. As for the back glass, just make sure no wires or other screws are blocking the back glass or that the slots on the back glass are not broken or bent.
since you cannot go up/down, can you go left/right? since you say that you have tested another screen, could be the logic board? you sure the iPod 4G was not dropped or has water damage?
did you check the alternator? battery cables intact and not damaged/broken? when you try to start, does it attempt to turn over or nothing happens? could also be your ignition is kaput. I'm not a mechanic, but something like this happened to my car and was told there was a problem with the alternator, luckily my car was still under warranty at the time.
Ok, if you have another battery, swap it out. also scrutinize the logic board and make absolutely sure nothing has broken off. some of those jumpers and resistors are extremely tiny. have you tried restoring using iTunes?
