After you wake up, talk to the Raven from Jukoli tribe (press number keys according to the on-screen prompts). Approach the door (left from the Raven - control the character with WASD keys). Hover over the door handle for the gear icon to appear - this allows to perform a contextual action. Press LMB to prod Kate to opening the door. They're locked.
Check out the button on the wall (right side from the door). Press it (another symbol) - it's not working. Move the cursor right to take a look (magnifying glass symbol) at the manual that's lying next to the box with the button - you have to be able to tamper inside the mechanism.
Approach the table in the center of the room and hover the mouse over the plateful of soup - click when an option of zooming in appears (magnifying glass symbol). Take the knife that's lying next to it (hand symbol).
Fix the door opening mechanism
Go back to the button box and while zooming in on it, press 'I' to get into the inventory - it appears on the left side of the screen. With the down arrow button alter the position of the knife, so that it's in the central (bigger) circle. Now click on the screw that's visible in the top-right corner of the box. You will use the knife. Unscrew it by making circular moves with the mouse.
After opening the box, you will notice that the green wire is not connected. Klick the loose end of it and attach it to the fuse box by holding LMB - the green diode has to light up. Now grab the upper section of the battery and slide it down into the sleeve with mouse. Then close the sleeve by holding LMB and moving the cursor upwards. Then press the glowing red button to open the door - Kate will automatically leave the room (achievement: End of holiday).