I recently came across an atrociously good deal with regards to two old Apple G4 iBooks. It should have been obvious why. One of them involved an intermittent error that was due to a loose hard drive connection. The other one was slightly more interesting. As has been discovered previously with others, the G4 has a design flaw with soldering on the graphics chip which means that over time, general wear and tear can cause certain pins to break loose from the logic board resulting in a now infamous startup problem whereby you have nothing but a black screen accompanied by madly spinning CPU fan. Based on existing research it seems as though there have been a number of solutions that have been tried.
Many of them require a medium to high degree of technical skill while some of them indicate a degree of desperation. It seemed to be indicated that pins 1/2 (which correspond to the power pins on the ISL chip) are the those which need to be resoldered. Howeover, if you do not have this ability you are advised to use a clamp the top and bottom of the section next to left side of the trackpad using a C-Clamp or even press down on it using your knee. Another option is inserting a piece of material between the foil and logic board in order to supply the required compression in order to re-align everything. While soldering is clearly the best technical/permanent solution you have to realise that the size of the solder involved is extremely small. Hence, there have been some who have advocated removing the logic board entirely and then putting it in the oven to have the joint re-weld itself. Of course, this is a boom/bust option that can either solve your problem or magnify it.
A few years ago I discovered a liquid silver emulsion material which could be used in linking broken electrical connections. It was a little too viscous for my liking though. I have since found out that a similar product which is less viscous has since been released called 'Wire Glue'. It cures in a few hours are provided you have a small enough brush is able to do the job that is required here perfectly and with a lot less risk than some of the other options that have been previously mentioned though.
For those who are new to Apple hardware you'll note that the actual packaging is significantly different than Windows based laptops (probably due to a stronger focus on aesthetics by Apple). On the G4 you'll be faced with an eternal plastic shell that can be quite fragile and you may be best using a thin plastic card in order to pry the case apart. Otherwise, you'll require an extremely sharp, small, and thin metal screw driver. You'll also find that one will require a variety of different screwdrivers apart from just flat and phillips headed shaped screw drivers.