If the laptop won’t power on (by battery or mains) then the drive will be removable and could be transferred to another via an adaptor - something like this:
https://amzn.eu/d/4qbeTvl
You just need to ensure you have the right adaptor type, some can be as a single adaptor and others as multiples
If the laptop tries to turn on but the drive is clicking then it’s the drive which is the problem - these may or may not be recoverable, sometimes they won’t start up the operating system but will manage enough for copying to another with an adaptor
Look up your laptop model on YouTube with a search on ‘change hard drive’ (if you can’t find the right one then a video for a couple of others could be good enough guidance)
Usually unscrew, slide and lift off a panel from the bottom of the laptop.
Perhaps also unscrew a securing bolt/screw then slide the drive to disconnect
Then load it on another computer, search around (note that files may not be in the most obvious place - eg ‘desktop’ would be somewhere such as \windows\users\my name\desktop)
Game save files could be in the programs area with the game or user file areas etc
You can potentially also just put the old drive into another instead of its own drive and startup / logon using your old machines user name - this will mean the operating system needs to detect and set up drivers for the differing hardware