The signal runtime of each cable has to be calculated or measured, so that an ordinary pushbutton can be used to trigger all 4 events and one doesn't have to send an event time. Therefor the runtim has to be known of each cable to add this to the triangulation calculations. If an arduino is capable of measuring runtimes in cables of 2m looping from and back to an arduino, this can be used instead of calculations. More informations are needed.
Cable propagation speed of signals is given by the formula as shown in http://upload.wikimedia.org/wikipedia/de/math/e/9/a/e9a0aa6d387b58b3f49b3302d4ffd84b.png To calculate the speed, you need the relative dielectrical constant (permittivity) of the insulating material of the cable, which is 2.4 for polyethylene. So, the speed of signals in a PP insulated wire is 1/SQRT(2.4) = 0.65 times the speed of light = 200,000 km/s. The relative permeability can be assumed to be 1 in this equation.
Practically, you can assume speeds of 20 cm per nanosecond. To measure delays in cables, you need a time domain resolution of few nanoseconds for 1 m precision. Assume you have a start-stop time counter, you should have 100 MHz to 1 GHz clock frequency for measurement of cable length. Try first with a pulse generator (50 ohm output, <10 ns rise time) and observe the signals at beginning and at the end of the cable to learn about how short it is.
For real measurement you need a high speed counter, running at about 200 MHz. This could be done with a fast PLD or FPGA with any microcontroller for display. A simple uC with 10 MHz clock won't work with sufficient precision.