The problem is common to this type of audio system. I would bet if you looked at the noise spectrum you would see 60 Hz plus many of the harmonic frequencies (120 Hz, 180 Hz, 240 Hz, etc.). The fact that it is more than just 60 Hz, or 50 Hz in some countries, is an indicator that it is not just simple ground loops.
I would also bet that your laptop power supply has only a 2-prong AC plug-- lacking the third ground plug.
In this type of power supply, the output is electrically isolated from the AC input. But it is not perfectly isolated. There is a small amount of current that flows between the isolation barrier. This is called the "leakage current". It is not a lot of current, but it doesn't have to be.
Some laptop users report getting shocked or having a tingling sensation in the legs when using the laptop while wearing shorts! The reason for this is that leakage current is going through the screws in the bottom of the laptop and into their legs. It sounds dangerous, but the amount of current is well below the safety limit. It is more startling than anything else. If you are wearing pants then you're insulated.
Laptop chargers that have the 3rd prong on the AC plug do not have this problem because that third plug is connecting the laptop chassis shield to ground-- forcing that leakage current to go to ground instead of into your leg. Of course, there is no leakage if you are running off of batteries.
In your case, the leakage current is not just going into your leg, but into your radio receiver. The solution to this is to properly ground your laptop.
You will have to experiment with this a little bit to find the best solution. Getting a power supply with a 3-prong AC plug is the best, but not always possible. The next option is to find something on your laptop that you can ground. Make an adapter from that 3rd prong to "something". That something could be the signal-ground on the output cable of your power supply. It could be a screw on the laptop. Or a shield on an unused laptop connector. Or the ground/shield on your audio cable.
Make that 3rd prong adapter, but leave the other end bare for the moment. Then start poking it around to see if or where you can connect it and have the noise go away. Once you have found a place or two, then finish up the adapter so it is easy to use.
Two warnings when doing this: Make sure that whatever you are grounding is actually ground! On the power supply output, make sure you ground the negative or gnd conductor. And when poking around, understand that you might actually have to poke a little hard. Both the bare wire and whatever you are poking will likely have a thin layer of non-conductive stuff on it, and you need to apply enough force to poke through it. Rubbing sometimes helps too. The non-conductive layer is sometimes paint on screws, or an oxide (rust) on the metals.
Oops, here is a 3rd warning: Be super careful when making that 3rd prong adapter. You're messing with potentially lethal voltages and we don't want you to die. Build the adapter in a way that there is no possibility of it failing and shorting out against either one of the other two conductors in the AC plug.
Give it a try and report back what you found!
Without a schematic I cannot determine if your grounding is correct, i.e. common ground, a common reason for some of the symptoms you describe.
Another point to consider is the liberal (correct) use of electrolytic capacitors and bypass capacitors.
Using a battery-only supply does not guarantee clean power supply rails. Are we sure the battery has adequate reserve available during circuit power up?
Given those conditions are properly met, you might consider the use of a "Supervisory" circuit for your processor.
MCP120/130
• Holds microcontroller in reset until supply voltage reaches stable operating level
• Resets microcontroller during power loss
• Precision monitoring of 3V, 3.3V and 5V systems
• 7 voltage trip points available
• Active low RESET pin
• Open drain output
• Internal pull-up resistor (5 kΩ) for MCP130
• Holds RESET for 350 ms (typical)
• RESET to VCC = 1.0V
• Accuracy of ±125 mV for 5V system
The Microchip Technology Inc. MCP120/130 is a voltage supervisory device designed to keep a microcontroller in reset until the system voltage has reached the proper level and stabilized. It also operates as protection from brown-out conditions when the supply voltage drops below a safe operating level. Both devices are available with a choice of seven different trip voltages and both have open drain outputs. The MCP130 has an internal 5 kΩ pullup resistor. Both devices have active low RESET pins. The MCP120/130 will assert the RESET signal whenever the voltage on the VDD pin is below the trip-point voltage.
They are available in TO-92, SOT-23-2 and 150mil SOIC.
Datasheet: http://www.mouser.com/ds/2/268/11184d-68220.pdf
Very handy little device for $0.60USD, or less!
Best Answer
The core of an isolated switch mode power supply is still, though cleverly switched, a transformer.
Thus, your problem is the same as this circuit:
simulate this circuit – Schematic created using CircuitLab
The whole point of an isolated supply is that there's not a single conductor from the primary to the secondary side.
Therefore, you can imagine the pair "OUTPUT+" / "OUTPUT GND" to have a defined voltage between them, but they float on a "random" offset relative to the primary side's Ground. That offset doesn't actually contain much energy, and you can break it down very easily, for example by connecting "OUTPUT GND" to primary ground (thus eliminating the isolation!).