Did you mean starting up the OS ( not installing it)?
You may have noticed that sometimes you can not power on and boot a MacBook Pro when it doesn’t have a battery installed. Let’s say you had to remove the battery of an older MacBook Pro…
osxdaily.com
Give it a read, I know your issue is different from what's described here, but read it nevertheless.
Since the MBP is very old, the battery is possibly faulty or has physical deformities. If you can hear the chime during boot up, the RAM modules, logic board etc are possibly fine. The HDD is possibly ok as it can boot up with the power adapter.
Try to source a battery specific to your model. 2012 MBPs also came with with non removable batteries.