Q: Why is my car stalling when I try and start it?

While the condition of your cooling system is certainly not healthy, it may or may not be related to the stalling issue. It is possible that due to the condition of the coolant, or merely coincidence, the coolant temperature sensor may not be sending the proper signal to the engine control unit. Engines need more fuel - a richer fuel mixture - to start and run properly when cold. If the engine control unit does not receive a proper signal from the coolant sensor, it may not make the fuel mixture rich enough to start or run properly when cold. Other components such as the mass air flow sensor, or even ambient (outside) air temperature sensor can cause similar issues. Also, if there is a vacuum leak somewhere in the intake system - sucking in too much air - this can effect the fuel mixture as well, causing the vehicle to stall. A broken/cracked air intake hose or leaking intake manifold gasket can cause this.

The best way to approach this, is have a certified technician look into the stalling issue to isolate the exact cause. Also, separately but as soon as possible, have the coolant leak and condition of the coolant addressed as this can lead to more severe issues.