TIP127 + TL074 power supply doesn't work until I touch it
Here are my thoughts: -


The TL074 has a common mode input range that does not include the negative rail (0 volts on your circuit) so, when you power it up the non-inverting input is breaking the rules and the op-amp cannot be expected to function correctly. Typically, anything between 0 V and 3 volt on the input will likely cause problems.
The TL074 has an output swing that does not reach the power rails so it's very unlikely that Q1 will switch off once it is on. This is probably what is mentioned in the question "until I try to turn it off".
Adding an extra level of voltage gain to an op-amp is usually a recipe for disaster (it turns into an oscillator) if not done carefully. Q1 is a common emitter hence it has plenty of voltage gain from base to collector. In this circuit, that gain could be in the realm of about 50 to the junction of R2 and R3. If you look at figure 9 in the TL074 data sheet you will see that increasing gain by ten is probably enough to make the phase margin zero (it becomes an oscillator).


Problems all round really.