Is there any way to feed a signal (line-in) into a mobile phone?
The TRRS connectors are wired like this, in order:


Tip: Left output
Ring: Right output
Ring: Ground/return
Sleeve: Microphone input


That way the headphones will work plugged into a normal TRS jack, too.

The microphone input is meant to connect to an electret mic with a circuit like this:

The bias voltage, resistor, and DC-blocking capacitor are all inside the phone.  So just connecting a signal source like a computer's sound card to the microphone input (with ground to the ground ring) should work.

If your sound source's DC output resistance is too low (normally a good thing), the phone could be interpreting it as a continuous button press (Answer or Play/Pause), because the headset button shorts the mic line's bias resistor to ground.  Does it do anything to indicate that it thinks a button is being pressed?  If this is the case, just put an electrolytic capacitor in series with your source, like 10 µF to 100 µF between your source and the microphone input.  This will block the DC current from the bias resistor while allowing the AC signal to pass.  Larger capacitance will have better low-frequency response.  

For instance, if the input impedance of the phone is 2.2 kΩ, 10 µF will have a -3 dB cutoff frequency of 7 Hz, which is plenty.