My fuji finepix z10fd won't turn on. I bought a

When ever any kind of unit, camera or other wise will not turn on, then there are all kinds of problems which could cause this. It could be in the battery circuit with something wrong or disconnected. It could be in the switch to turn on the unit. There also could be a number of other things which could be at fault all of which could cause the camera not to turn on.
If there is some thing which happened in the past such as an impact, water getting inside the camera, or from being dropped, all of which could cause trouble.
My suggestion is to sell it on a site such as Ebay as parts, or have it looked at (if it is worth it) by a repairman.

check the micro switch in the door/flap where the memory card goes has not stuck