It could be a few things, it could be any combination of software and/or hardware issues but, my first thought is that your computer(s) don't have the minimum required version of iTunes, which is version 10, you can download the latest version of iTunes here for Mac or here for Windows. (you also need to make sure your computer(s) meet the minimum requirements for iTunes 10 as well). My second thought is that your computer(s) dont meet the minimum operating system requirements for your ipod shuffles which are: Mac system requirements Mac computer with USB 2.0 port Mac OS X v10.5.8 or later iTunes 10 or later Internet access is required; broadband recommended Windows system requirements PC with USB 2.0 port Windows 7, Windows Vista, or Windows XP Home or Professional or later iTunes 10 or later Internet access is required; broadband recommended
you might have to reformat the hard drive. your files might have gotten corrupted or the temporary files from all your previous songs havent been properly deleted. reformatting or restoring it to factory settings should fix the problem
that sounds like a huge undertaking, if your up for the task, you probably need to replace most of the innards except for the outer case and hard drive, the circuit board might be salvageable. if it were me id get a new touch and save the other for a rainy day project.
resetting the PMU is a great idea too. when you do get it to turn on you need to open your system profiler and on the left hand side select "power" and it will tell you the health and capacity of your battery and see if your power cable is working as well.
try removing the battery, plugging it into a wall and then see if it starts up. If it does then the capacity of your battery is dead. the battery lights do not indicate the capacity of the battery it indicates the amount of charge the maximum capacity of the battery. so you could have full lights on your battery and only have 200 mAh. then you just need to buy a new battery or take away all the perks of having a laptop and use it without a battery If you decided to get a new one, you need to fully charge and then fully drain the battery every time to get the maximum life out of your battery. Leaving your ipod, laptop, iphone(or cell phone) or pretty much any electronic device plugged into a power source all the time is a terrible idea, it will kill your battery years before its lifespan.
if your radio plug in charges it as well, and you keep it plugged in a lot it sounds like you killed your battery. I wouldnt suggest trying to replace the battery, getting into the nano's without breaking something is more trouble than its worth. here's a link to the battery replacement guide (the guide even says it is Very Difficult): iPod Nano 3. Generation Akku tauschen If you decided to fix it or get a new one, you need to fully charge and then fully drain the battery every time to get the maximum life out of your battery. Leaving your ipod, laptop, iphone(or cell phone) or pretty much any electronic device plugged into a power source all the time is a terrible idea, it will kill your battery years before its lifespan.
if you use the guide for your powerbook g4 aluminum 12" 867mhz to remove the logic board, follow steps 1-25 and it will show you how to remove the hard drive. then just follow the steps backwards to install the new hard drive. here is the link to the correct guide for your computer, PowerBook G4 Aluminum 12" 867 MHz Logic Board Replacement