A friend of mine asked me to repair a TI-84 Plus C Silver Edition. When plugged into the charger, the orange charging led comes on for about 5 minuts then turns green. Upon disconnecting, the battery is at the 70% level and drops off to 0 again within 10 minutes. After testing on multiple chargers and resetting the memory, the issue persists.

I'd like some advies as to whether I should check the hardware or software first since a replacement battery is $15 and the OS is unavailable on TI's website for reinstall.

I'm by no means the expert on hardware, especially calculator hardware but this sounds kind of like a faulty battery that can't hold it's charge.

I agree that this sounds like the battery can't hold its charge.
As for the OS, Xavier (Critor) has been painstakingly keeping track of pretty much all OSs released by TI, and makes them available for download on ti-planet. Here are the CSE OSs
Ti have been furtively erasing the CSE from existence, almost claiming that it never happened

You can also find a copy of the most recent (and probably last, at this point) OS version at the Internet Archive.

I just tried reinstalling the OS using the TI-planet links, calculator still broken unfortunately.
Therefore, I'm ordering a replacement battery soon. (15$ is tough to save up in college)

Thanks for the advice.