Hi @azzyazrael
Connect an external monitor (TV?) to the laptop's HDMI port and turn on the laptop.
Once you think that the laptop has started and booted into Windows, press the Fn and F9 keys (both together) and check if there's a display from the laptop showing on the external monitor. You may have to press the key combination a few times just to make sure as it toggles the display output from laptop screen only, to external monitor only, to both on together.
If there is then there's a problem with the video circuit to the laptop screen in the laptop. Try shining a flashlight at an angle close to the laptop screen and check if you can see any images on the screen. They will be very faint if they are there, so try this in a darkened room. Also make sure that you have switched the display output back to the laptop when you try this i.e. no display on the external monitor.
If there isn't, then the laptop may not even be starting even though the power light is on.
Do you know if the motherboard was cleaned at all by the repair shop?
@azzyazrael
OK.
If there's no display showing on the external monitor or if you can't see any faint images etc, you will have to open the laptop and inspect it for corrosion etc caused by the cat vomiting on the laptop.
Here's a video that shows how to open it and also how to disconnect the battery from the motherboard.
Disconnecting the battery is necessary because there's always power on the board even when the laptop is turned off, and any liquids coming into contact with electricity can cause damage and corrosion to the components. The corrosion is ongoing until it has all been cleaned away, so the earlier you clean it the more chance there is of saving the laptop.
Here's a link that in general describes what to do. Electronics Water Damage
Once the motherboard has been cleaned then reconnect the battery and check.
Be careful when cleaning as you don't want to cause any more damage than what there already may be.
You can only try. Either that or search for a reputable laptop service service that is experienced in liquid damage repair and ask them to fix it.