That would just be my luck, too. The price you pay just to own a physical copy.
On occasion you can replace that internal battery (normally a large flat watch battery) and be able to save your game again. I was able to do it to a few games, there was one or two common games I recall that didn't work after I replaced the battery. That might be due to improper installation or sparking something across the finger board inside the cartridge. I'd say to use the Emulator version and find a NES controller fitted with a USB cord. They work wonders, best of luck!
Also, I prefer the NES version myself, I'm old and I enjoy the classic modern times of my youth. Young whipper snappers!
- I'm getting sick of this! Thou art such a pain in the...! Confound it all! I'm starting to talk like you! - Sabin (FFVI)
- Shut up! You spoony Bard! - Tella (FFIV)
I actually appreciate the original game's difficulty since every version from Dawn of Souls onward is so easy that you are practically never in danger. This is why I recommend the PS1 version since you can play it on its original difficulty with the spells fixed and with more modern conveniences (better menus, retargeting enemies, quick saves, etc.).
Some of us old timers have to have that NES flavor sometimes, though.