Unfortunately there is some merit to what Choof said above.
I would argue that the the status of the laptop wasn't in 'pristine condition' if it was sitting in one place being neglected for 10+ years. Battery is almost certainly dead at this point. If you've got an external battery, remove it and run it without it. If it's an internal battery, open it up, unscrew it, and unplug it from the motherboard. You're not going to be using a 10+ year old battery in any good condition here.
If it still doesn't power up after holding down the power button for 3 or more seconds while plugged in, WITHOUT any batteries connected, we write the system off as 'fucked'. It'd be cheaper and faster to get a refurbished laptop than to troubleshoot something that old.
If you really need data from the computer, you can pull the hard drive for the laptop by unscrewing the back of it, and then get a caddy or external cable for it, something like this:
https://www.amazon.ca/s?k=SATA+to+US...f=nb_sb_noss_1
Just double-check connectors on the drive. Pretty sure with 2010/2011 model stuff you're still going to be working with hardware that's removable. Don't think they did eMMC technology yet for flash storage soldered to the motherboard.
Source: I fix computers and laptops for a living as a professional.