You can still get decent batteries on Amazon for Samsung SIII. I was using an SIII until February 2023 (screw you, AT&T) and it held enough charge for a day and a half standby, or a full day of average use, about the same I got from my first in 2013.
Old doesn't mean bad. I don't know why all of a sudden something being old means it's useless to people here. A lot of times, the older stuff lasts longer, and is far more repairable, and oftentimes has many more features than the 'modern' versions. If anything, modern tech encourages disposability (see: laptops glued together, soldered RAM, non-removable batteries, smartphones: non-removable batteries, OEMs against right to repair, Apple iPhones having screen replacement DRM that disables Touch ID and so on)
disposable =/= sustainable
Also, a phone from 2012. Not old. 2012 ain't that long ago. Is anyone left around anymore who remembers when something had to be 30 years old to be 'ancient?'
For the OP:
The Samsung Galaxy SIII requires a battery to power on. If you connect the cable to a charger without a battery it shows a screen saying it needs a battery. You can't get past that by holding the power key.
Sadly, the Galaxy SIII isn't VoLTE (Voice over LTE) compliant, and is essentially a wifi-only glorified Galaxy Player today. Putting a SIM into it might even hotline the SIM due to network incompatibility (AT&T actually hotlined two, one that was in mine originally and a new BYOP that I tried after, shortly after getting a text message within 5 minutes telling me it's not supported (ironically it was working for those 5 minutes prior fine so is it really not supported, AT&T? Or do you just hate vintage that much?))
the earliest phone that is a Samsung that can work with VoLTE/Wifi Calling/HD Voice is some specific variants of the Galaxy S4, and all Samsung Galaxy S5's.
If you truly want to use an SIII as a phone there are means to work around this. One that I know for sure is putting a data-only SIM into it (for a 'tablet plan') and use VoIP calling apps that are supported by the version of Android on it. There are a few left on Play Store, and I was able to use my Note II as a phone on Wifi with one of them (Freecall) and these apps work with data or Wifi. Google Voice is no longer supported, I've tried. It did work, last year. Another app that works is Viber. It costs a few dollars to dial any phone and not just Viber contacts, per month, but it's cheap. (Viber Out subscription)