This may be a very naive answer, but I've had both the problems you're experiencing, although, not at the same time.
My trunk wouldn't pop because my knee accidentally hit the button on the right side below the steering wheel, which you can switch on and off, a valet protection feature.
And also, if you happen to be using the valet key, it won't work in the trunk, you have to use the above described button to open the trunk.
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the trunk won't pop - 
