Simple troubleshooting (individual things you can try): Plug charger into the laptop and try booting with that. (Look over to the side to see if the LED battery indicator is on while you are at it) Hold the power button. Sometimes that works. Check to know if your laptop is not coming to life at all or if it just isn't booting to the operating system. (if you can get into the bios, that means your system works, but booting into the operating system has issues for some reason that may require further troubleshooting)
I do not think the power jack needs to be exactly the same model number. Usually a power jack that's compatible with similar model number laptops should work with yours. For example, I have an HP Pavilion all in one going under 24-b237c. However, components that are compatible with 24-b2xx (replace xx with another model) should work with mine.
I am not sure about the upgrading part, but you certainly can replace the SSD chips. However, the NAND chips are soldered onto the board, so you will need soldering skills and a rework station. I myself haven't done a NAND replacement yet. If you are looking for a NAND chip replacement, look at the SoFix MacBook repair website (masterliuonline.com). They have original NAND chips, and they have A2251 model.