My iPod's power button only works when the iPod it's turned on.

Recently, after a dreadful fall to the ground, my iPod's volume up button got sort of stuck, and all it did was turning down the volume instead of turning it up.

While trying to repair it myself, I broke the headphone jack assembly connector (never disconnected it from the logic board, ripped it off while getting it of the body, total genius work), so I had to buy a new assembly.

After many tries, I finally managed to mount the assembly properly, and it works as it should... Except that if I try to power on the iPod when it's shut down (after long-pressing the power button), it won't do anything, so the only way to turn it on is by plugging it somewhere.

All buttons operate correctly when the iPod is on, including said power button. I have no need to keep the thing plugged in to use it, I can disconnect it as soon as it powers on, so I have no battery-related issues (or so do I think).

What can it be, and how could I fix this?