Used 2004 Aveo Hatchback Help

So i just purchased a aveo3 hatchback with 166000km and no timing belt change, probably the first thing on my list. Just a few weird quirks the trunk does not open properly, the handle when pulled in just sticks and I have to pop it out. Second the car came with a remote with locks, keyless start, and trunk, the only option that kind of works is the starter but as soon as i get in it shuts down, the locks and trunk buttons when pressed just turn the lights on and of and does nothing, Could the car not have power locks but still activates the lights and dash lights as if it were working. any suggestions would be great.
Thanks

the latches / motors could have worn out?

you basically need to open it up check the parts are not rusted and binding, and free them up, clean them and reconnect them with enough grease so they work.