Use USB as an on-off switch
There's pretty much no chance you'll get all this for $4, it is not a realistic budget for this. But that's not to say it's not possible.
You do need a microcontroller with USB functionality (or have it bit-banged, but USB ones are cheap enough) to talk to the Android phone. Then the Android phone could use its USB API in the SDK to talk to it and issue a command. When the USB microcontroller recognizes the 'take picture' command or whatever, it could flip a transistor on/off to toggle those wires you have and tell the camera to take a picture.

But you mentioned an 'old' Android phone, that could be a problem because only newer ones running Android OS 3.0 and up have the ability to expose the USB API to talk to it. If your target phones don't run that, this isn't going to work.

In that case, to accomodate most Android phones, even older ones, you could do this over Bluetooth. But that's going to raise your costs even more because you'll need a bluetooth module and power source for the Bluetooth, probably a battery, on top of the micro.
But Bluetooth modules can be very cheap, here's one for $5.50 USD and they're even less in larger quantities: http://imall.iteadstudio.com/prototyping/basic-module/im120723010.html

Otherwise an even simpler approach with no micro could be making a circuit with a photosensor such that it triggers the camera wires to cross when it detects some amount of light, you could vary that with a pot/resistor. Then tape/connect the photosensor somehow to your phone and program it to light up the LCD or the flash on the back (if it has one) when it wants to trigger the photo. That might be do-able for under $4 but it's not very elegant.

Good luck!