this might be what you are looking for:
while it is really for turning the computer on/off, you might be able to use it to turn on the amps after the computer is booted up.
one of the features is that it senses wheather the computer is turned on, this might cause problems keeping the amps turned on. but no one knows until it is tried.
if you would like to build a circuit, there is always a time delay circuit:
Iíve selected the 555 timer due to following reasons.
1. Timing from microseconds through hours.
2. Ability to operate from wide range of supply voltages.
3. High temperature stability.
4. Easily Available.
5. Its triggering circuit is quite sensitive.
This is basically a monostable. The external timing capacitor C2 is held initially discharged by the timer. The circuit triggers upon receiving a pulse to its pin 2 when the level reaches 1/3 Vcc. Once triggered., the circuit will remain in that state until the set time is elapsed or power to the circuit cuts off. The delayed period in seconds is 1.1 C2.R1 where R1 is in megohms and C2 is in microfarads. In practice, R1 should not exceed 20 M. If you use an electrolytic capacitor for C2, select a unit for low leakage. The time delay may have to be adjusted by varying R1 to compensate for the wide tolerance of electrolytics.
from this page, 4th item down.