Sounds like a pinched/damaged or not fully connected at one or both ends.

Did you attempt to "jailbreak" your iPhone? Try to restore your iPhone with iTunes and see if that fixes the issue.

The battery may need replaced. It's possible that when you fixed the screen static electricity may have damaged the battery or something else on the mainboard.

No need to get rid of the iPhone due to "Home" button malfunction. Search Google for "iPhone home button repair" you will find the part(s) you need. Make sure you get the correct button (2g, 3g, 3gs). Update: No need to vote down. I didn't post links because I wasn't sure if it was allowed. You didn't say if you had a 3G or 3Gs, I will assume you have a 3G. Easiest way to change the home button and circuit is to get a complete top (digitizer, glass, home button, etc). Just use ifixit's tear down guide to disassemble and reassemble. Here is a Ebay link to the unit: http://tinyurl.com/yzhnfe5 It may not be the cheapest solution ($67.99 USD), but it will be the easiest. *Please vote up if I've helped

You are correct about the green wire needing to be soldered. Headphone wire is a major P.I.T.A. (lol). If you can get some fine sandpaper rub the end of the green wire to get some of the coating off. Tin the end of the wire and hold it with some tweezers (it will get hot quickly) and solder it to the headphone plug. Sometimes holding the wire against doesn't make a good enough connection to test, due to the protective coating on the wire. The string I believe is there to provide some protection and flexibility to the cable. Good luck!

Upgrade to the newest firmware on both PS3s and there will be a new utility in the settings that will allow you to copy all of your files from one PS3 to the other using an ethernet cable (you can even transfer copy protected files and game saves that don't normally allow copying). You cannot just remove a hard drive from one PS3 and put it in another and expect all information to transfer over. You will have to format the drive.

If you cannot find the ID you could replace with the same value and type.

The bearings in the fan may be going bad. Something may be touching the fan.

Does it turn on? Will it charge? Does your PC or Mac recognize it?

The connections to and from the battery are soldered. Coming loose is a very slim possibility.