If you are hoping to get your machine running again for standard use, you may be able to find a local Apple repair shop who can do it for you but it likely will not be a cheap repair.
Apple “might” be able to fix it at a service center if you can get a Genius Bar tech to take pity on you, I’ve had mixed results on this front as Apple would much rather sell you a new machine.
If you are simply interested in getting at your data so you can migrate, the 2011 MBP is easy to open and the hard drive can be removed quickly and plugged into an external USB SATA reader and your data or even the full drive set up can be retrieved/cloned.
ifixit.com has good instructions on this as well as tool sets if you need a specific proprietary tool for opening the laptop.
Amazon, among others, has the drive readers.
WEme USB C 3.0 to SATA External Hard Drive Dock Docking Station, SSD HDD Disk Duplicator Cloner for Dual Bay 2.5 3.5 Inch SATA I II III, Support UASP and Auto Sleep and 2X 12TB, Black https://www.amazon.com/dp/B07PX2HHD6/ref=cm_sw_r_cp_api_glt_fabc_V9YYQGE3KY0X8H7B4SHJ?_encoding=UTF8&psc=1
WEme USB C 3.0 to SATA External Hard Drive Dock Docking Station, SSD HDD Disk Duplicator Cloner for Dual Bay 2.5 3.5 Inch SATA I II III, Support UASP and Auto Sleep and 2X 12TB, Black https://smile.amazon.com/dp/B07PX2HHD6/ref=cm_sw_r_cp_api_i_CDR468GZYVKA1F9XYBNS
Get one of these and another hdd and see if you can recover your data. I have seen it before the sata connection inside the case comes loose after a fall.
Maybe I misunderstood your requirements but why not just use a HDD dock if its all external? There are loads out there, this is just an example.
WEme USB C 3.0 to SATA External... https://www.amazon.com/dp/B07PX2HHD6?ref=ppx_pop_mob_ap_share
Plug drives in and hit the button and walk away. Not free but easy