An easy solution would be useing a simple switching transistor... I am thinking something such as a 2N2222 NPN General Purpose Tran. would work..
It can handel around 60v on the base (DTR output) which is well over enough and can put out as much as 40v on the emitter side (To amplifier)... The only possible problem I see could be it can only handel up to 800mA of current at the collector (12v input to turn on amp)
I am not sure if that would be enough to turn on the amp or if the transistor could even handel being hooked into a car electrical system? Anyone have any ideas on this... I can test is later if need be...
Simple diagram of this application if it would work is
*note* the transistor is quiet small (excluding the sire leads the actual chip is smaller than your pinkie nail) the size on picture is just for referance...*
**Edit**
As this is a simple cheap way of doing this I would suggest the use of an opto-isolator in this case for added protection of the PC... If this would work and someone would confirm it I will try it in my Van (normal system) just to test the therory...