I was just reading this and thought I would share experiences I've had with these modules.
Some times the pin positions are not correct which means that you may have to do some testing and relocate some of the pins to get things to work properly.
I've had to do this with quite a few GM vehicles even though the module is listed as the correct one.
First thing I would do is forget about the module for a second.
Probably the best way to test, would be to plug in the factory radio and test the wires with it Off then with it On to see for sure which wires are the remote turn on and which wires are the power wires.
Just remember when doing this test that the 12volt switched accessory will probably only show 2-5 volts cause its Data (Databus). Also a test light is Not recomended for this car only use a DMM.
Then unplug the Factory HU and compare the factory harness to the harness in the module to make sure the corosponding pins are in the correct location.
You could also jump out the remote turn on wire in the factory harness with a jumper and then try to pop one set of the speaker wires with a 9v battery. Do this test with the Ignition in the On position.
This sounds to me like one of two things either the amp is not getting the signal to turn on or the Databus wire / switched 12v wire, is not in the correct position in the harness.
Usually I use Periphrial modules at work which are basically the same thing just a different brand.
Does this module have a speaker built in that makes the chime noise in place of the front left ?
Does it have a LED that lets you know that its powered up with the 12v switched wire ?
92 Bonneville SSEi - Stock - Remaining repairs needed due to neglect by previous owner - ABS/Trac, AC.
Mods so far: Maganflow High flow Cat, Rebuilt */C
Future Mods: Interior swap for Leath, High Output Altenator, Crazy system, Climate Control swap & Custom Exhaust/Intake.
98 Dodge Stratus - Wifes Daily Driver
92 Dodge Shadow - My Winter Beater