Yesterday I designed this circuit (in a hurry) for an old box. The goal was that the CPU will start a few seconds after the box is powered on (reset is inverted). The secondary goal was that even if you switch the box on and off quickly, the delay will start again, so a simple RC won't do it. This schematic actually works, but I'm wondering if there is a more simple solution. My idea was that C1 can discharge faster through R2 which is smaller than R1, because D1 will be conductive when the power supply is missing. The problem is that the smaller R2 is, the faster C1 can be discharged but the more supply current the circuit needs.
mypc\\temp\curcuit100.png