Both of the 12v rail shut off problems, the car audio amp load shutoff when connected and the PSU shut-off when the 5v phone charge load is disconnected maybe related to the PSU you are using. I am having a similar problem when I use the 12v rails to power 12v tungsten under cupboard lights to light my Kitchen counter top. The lights are 12 v 20 w and run at 1.67amps each. I have 6 of them powered so they need 10 amps total to run. Per LT SPICE model of the 20w lamp, the lamp has an inrush current of about 27 amps each at start up, which quickly drops logarithmically to 1.67 amps with in about 1 sec.
I found this possible solution at
http://reprap.org/wiki/PCPowerSupply#Troubleshooting
Electronics prepared for PC Power Supplies
Base Load
12V halogen as 5V base load.jpeg
Many PC PSUs (not all) require a base load on the 5V rail to work properly. Connecting an old CD drive or a 12V light bulb (into the 5V rail, see picture) are well proven methods to get this load.
Wether you need a base load or not has to be tried. If even tiny loads on the 12V rail cause the PSU to turn off, a base load is required. Also, a base load never hurts.
Here is some additional discussion on the arduino boards.
http://forum.arduino.cc/index.php?topic=113338.0
PS Update: I hooked 20 w 12v lamp to 12 v rail without the 5v rail load. The lamp briefly lit and the power supply shut off. I reset it by turning the power switch Off (o), disconnecting the black to green jumper (Power turn on). I then hooked up another 20w 12v lamp to the 5v rail red to black, turned the PSU switch back on ( I ) and the lamp on the 12 v line stayed on. It is still lit now after about 10 minutes. SO that must have been the problem. No 5v Base load. I do not know what the minimum base load is to keep the PSU regulating. If any one knows please comment. BTW running an ALTEC BP500U 500 watt PSU.
Here is a little more info about 5v and 12v rail loads for proper operation of the ATX PSU.
http://www.epanorama.net/links/psu_computer.html
Using PC power supply as general laboratory power supply
Many people seem to have nowadays many old PC power supplies from old comouter aroudn them and seem to want to use them for some other applications. The PC power supplies supplies many voltages (+-12V, +5V etc.), but using those power supplies successfully takes some knowledge. The PC power supplies are generally switched mode power supplies that do not like run without a load (power supplies usually automatically shut down themselves then they see no load). The AT standard power supplies do not have any special signalto stay on. They are designed to work on certain power loadsrange correctly. If they are loaded less or more than they are designed to work they will shut down themselves. Generally you need to load the +5V output enough (usually 1 amprere to many ampreres minumum load needed depending onpower supply unit, youy might need to test this).The motherboard or old hard disk connected to power supplytakes at leas this minimum load, so keep the power supplyhappy. If you do not want such devices near you, you need to have some other type of load you can use, for examplewell cooled power resistor to +5V output or a 12V car headline bulb connected to +5V output (12V bulb willglow red/yellow when powered with +5V and take enough powerto guarantee that minimum needed load). The minimum load on +5V is needed, because PC power suppliesare generally regulated at +5V output. The controllign loopon the switching power supply works well on normal load conditions, but in case of too little load causes generally the+5V output to rise to too migh voltage, which leads to theshutdown of the power supply when it detect the overvoltage. Whatever power supply you want to use the best approach is tocheck the PSU spec: some require a minimum current draw on some rails. It is quite easy to provide this by means of a power resistor or power resistors. What is said above is usually valid for most other computer power supplies as well.All modern PC power supplies are nowadays built to match the newer ATX standard. Those power supplies have more signals on their connector for example for turning them on and off. If you plan to use this kind of power supply, you need to take care of the minimum load details told above. In addition to this you need to find out the details how you are supposed to turn this kind of power supply on. To activate ATX power supply, only PS_ON is needed. PS_ON can be activated by connecting ATX power output pin 14 (PS_ON) to pint 15 (ground). Some ATX PSUs also require a load on the main +5V to start (could be even damaged without enough load). Most but not all require a load on +5V to regualte properly, a few require aload on +12 as well. PWR_OK signal has nothing to do on ther controlling of ATX power supply operation. PWR_OK is an output from the supply. "PWR_OK is a "power good" signal. It should be asserted high by the power supply toindicate that the +12 VDC, +5VDC, and +3.3VDC outputs are above the undervoltage thresholds.