Yeah, your right. We have both numbers.
But the 3.3 would explain why the Darlington didn't work either.

When we want to use the Darlington works as a switch then it is get into a bad situation, the situation maybe like these -- because only the second bjt could works as a transistor switch, but the first bjt is works as two diodes, so the second Vce of njt as Vce2 = Vin - Vbc1= 1.4V-0.7V = 0.7V, W2=Vce2*Ic2=0.7V*3.5A=2.45W, so you can see it why it is getting hot, when the Ic is higher then the Vce also will be higher.

I was tested the situation of darlington pair as above, but I didn't test the circuit as TIP120, probably it has a better situation.

 

When we want to use the Darlington works as a switch then it is get into a bad situation, the situation maybe like these -- because only the second bjt could works as a transistor switch, but the first bjt is works as two diodes, so the second Vce of njt as Vce2 = Vin - Vbc1= 1.4V-0.7V = 0.7V, W2=Vce2*Ic2=0.7V*3.5A=2.45W, so you can see it why it is getting hot, when the Ic is higher then the Vce also will be higher.

I was tested the situation of darlington pair as above, but I didn't test the circuit as TIP120, probably it has a better situation.

If he only uses 3.3 volts and the Vbe of the TIP120 is 2.5 volts, that only leaves .8 volts across his 220 ohm base resistors - less than 4ma. With an Hfe of 500 to 1000 that's just not enough for 10 amps.

 

So @adam450. What voltages do you have available.
What is your micro?
Are you writing your own code? So you could make a high or a low the on state?
Are you testing the solenoid with the plunger in it?