First off, if you have a display and the touch screen works then the screen is all good. Just to be clear, do they still functionally work when touched? Or do they just not light up anymore? Or both?
Now, there is the small chance you left some adhesive plastics over the bottom of the glass the screen is attached to not allowing the light from the soft keys to shine through the glass.
You could have also potentially tore or damaged the soft keys themselves when removing the old screen.
I would be very careful and just remove the screen and see what's up, even post pictures if you want.
I doubt you have a press to press cellphones with, so taking the stuff back apart should be easy, just be very careful and take your time when removing the screen again.
When you take the screen back off you're going to notice two thing flaps on either side at the bottom that wrap around the housing and are attached to a PCB board at the bottom of the phone, where the USB port is. If you tore them, then you'll have to replace that PCB board, they are about a $20 part or so. If that's the case I'd keep the phone apart until you get the parts, make sure you put both the screen and parts in an ESD bag to prevent any damage.