Ok good question. You have done all the basic steps i would have taken as well what I would do to further isolate the issue is hook the computer up to an external display and see if that gets a picture when the issue is occurring. If it gets a picture even when the internal display is not than you can rule out an issue with the video card. At this point either the issue would have to do with the display or the connection of the display to the logic board. Keep in mind this is just speculation on my part but hopefully it will give you something to work with. Good luck, Xen

Ok there is a couple different reasons why this could be. First, if the songs are unchecked it is normally set to just sync checked songs and playlists. So checking the songs may resolve the issue. Secondly if it is just purchased content that is not syncing you may need to authorize your mac through itunes to play that media and sync it to the ipod. You can authorize the computer by going to the store menu in itunes than to authorize computer in that menu. Xen

Ok if you bought this one in late 08 than it is 4gb of ram. If you purchased this in mid 09 than it is the 8gb max. Since you said that this is the unibody model with the built in battery it would have to have been the mid 09 model so on yours I'm gonna say 8gb is your maximum amount of ram.

According to what I can find on this it should remove the same way as the prior iPhones sim card. A paper clip should be a decent substitute for the sim card removal tool that came with the iPhone. The following article is from Apples knowledge base and has a guide as to how to remove a sim card. http://support.apple.com/kb/ht1438

One thing you should try is to attach an external display and see if the issue transfers to the external. This will let you know if it has to do with the video card directly. If the video processor is at fault the external will have the lines as well.

The question mark means the computer is not finding a volume that it can boot off of. If you can boot to the OS install disk check disk utility and see if A. the drive is shown and B. attempt to repair the volume if it is showing up here. Provided the drive shows a repair disk could get you up and running. If the repair fails though it is a reformat and reinstall of the OS. If the drive is not shown than you want to reset the SMC/PRAM and than see if the drive is shown afterwards. Xen

Try resetting your PMU. This is done by simultaneously pressing and then releasing Shift-Control-Option-Power on the keyboard. Also try a PRAM reset by holding command, option, P and R during the boot process. If neither of these options work I would recommend trying to attach an external display to see if that gets any image. If the external display gets no picture your issue most likely has to do with your video card. Xen

You do need a card to setup an itunes store account. As for the iPod touch it does not require a credit card to sync content with the computer. If you give us some more information as to where you are in the setup perhaps we can help you through the rest of it :) P.s. itunes on the iPod touch requires a store account to use.

You could always just reformat the drive through disk utility. I think this will probably be the best bet in this situation.

If you continue using the power button to shutdown it can cause issues with the operating system. Eventually it is possible you will have to reformat and reinstall if the OS gets corrupted. As far as solving the issue the 1st step I would do is test in a new user account. This will let you know if you're looking for an issue with your user or something with the OS/hardware. After you've tried this let us know the result and we can provide additional steps for you :)