These problems all stem from one thing: heat. The early P4 prescotts used in these Dells were simply too hot, and consumed too much power, especially in conjunction with a decent graphics card, for the stock PSU to handle in the hot environment. Dell's stock cooling solution was inadequate for these Prescott CPUs. Dell chose quiet operation over effective cooling, and the price to pay for such a decision is rapid component failure, namely the PSU, CPU, and mobo. Dell's earlier Dimension series, the 4500/4550 line and 8300, did not suffer these problems, as they were equipped with cooler running Northwood P4s.
Also, sucks that you all own Dimension 8xxx series towers. Their proprietary mobos make it impossible to put in aftermarket mATX mobo, or to put the factory Dell mobo into a better ventilated aftermarket case. You could try an get a mobo tray from a Dimension 4500/4550 series, as it supports aftermarket mATX mobos, but even then the unique all-in-one front panel connector is a serious hurdle to overcome. In short, the Dell 8xxx series, and especially the 8400, are poorly designed computers.