How can I calculate the minimum thrust to weight ratio required for a given takeoff distance?
Assuming you know the mass $m$ of the aircraft,  the speed $v_0$ required to take off and the lift and drag associated.
Using basic dynamic and newton's second law you can calculate the average acceleration $a$ required to reach take off speed before the end of your runway:
$$a=\frac{v_0^2}{100\text{ft}}$$
Then using your drag generated at takeoff to be on the safe side
$$\text{Thrust} = m * a + \text{Drag}$$
Implying,
$$\frac{\text{Thrust}}{m}=a+\frac{\text{Drag}}{m}$$