Might want to make sure both units are not affected. This is the range of serial number from the now-defunct Apple Repair Extention Program for USB 2.0 eMacs:
- G8412xxxxxx- G8520xxxxxx
- YM412xxxxxx - YM520xxxxxx
- VM440xxxxxx - VM516xxxxxx
A "collapse" is more indicative of a video cabling issue, but the bad caps produced such a wide range of problems that it's hard to sort through them.
If the old eMac is a USB 2.0, which a 2004 unit should be, the HD should exchange with the new one. As the last of the eMacs shipped with Tiger, the new computer should have no probelms with a 10.4 boot volume on the old drive. You can upgrade to Leopard one you have hte new disk in place.
NOTE: Takeapart and reassembly on the USB 2.0 must be done "just so" or you can permanently damage the power switch. Instructions for the USB 1.1 takeapart are slightly different , and the power swtich damage is usually caused by people using the older instructions on a newer eMac.
If you are not up to the takepart nor can you find a local computer tech who knows these. consider taking the drive out of the dead computer(won't make much difference if you damage that one as it's dead), buy an external Firewire enclosure, and put the old drive on it and use it to move data to the new computer. Then you can leave the external attached as a backup drive.
Is the new one a 1.42Ghz model? They have been practically trouble-free around here. We have one and it's been rock solid since we bought it as a refurb in Jan 2006. The 1.42G has the advantage of a Core Image-enabled video chipset, the ATI 9600.
And all USB 2.0 eMacs can, with modern memory modules, support up to 2G of RAM.