I bought broken Mac and I need to repair it.

Personally I would focus on getting HDMI and trackpad to work before you touch the display. To get HDMI to work you may need to boot into clamshell mode which is when you have external keyboard, mouse and AC adapter with the lid closed as these machines won’t have display out on HDMI when lid is open until after boot and graphics is initialized. More than likely you just need a new trackpad as that is a fairly common issue on these Mac’s. The displays are pretty expensive so that would be the last thing I would get after verifying full functionality.