As best as I can tell, there is no such thing as a TI-84. There are:

TI-84 Plus
TI-84 Plus SE
TI-84 Plus C SE
TI-84 Plus CE

Others?

I'm guessing that you tell which is which because it actually says so above the screen?

Which (if any) flavors have a "Reset Button on the Back", as so many URLs mention? I don't see one on mine. There's a 'dent' to the right of the little plate covering the backup battery, but no button.

It takes 4 AAA's for power, and I guess that is why it just refuses to turn on when I plug an (apparently TI-84+ official) charger into the USB Port? wikipedia says only the C SE and CE have rechargeable batteries.

Yes, of course. Anywho, based on that information, it appears you either have a TI84+ or a TI84+SE. If you have any more questions, feel free to ask!

Those are the ones which can not be charged. The "reset" button for ti 84+ is generally removing the batteries.

Here http://www.cemetech.net/tools/index.php at the top right is a picture of most calcs mentioned in your post. You might be able to see which ones are which?

For fun, here's the complete list of TI-84s AFAIK (ignoring different colors/revisions/ez-spot versions)

TI-84 Plus (2004, International)
TI-84 Plus Silver Edition (2004, International)
TI-84 Plus Pocket.fr (2011, France)
TI-84 Plus Pocket SE (2012, Asia)
TI-84 Plus C Silver Edition (2013, International)
TI-84 Plus CE (2015, North America (AFAIK))
TI-84 Plus CE-T (2015, Europe minus France (which gets the 83 Premium CE))
(Then, there's also the TI-84 emulated in the Nspire non-CX non-CAS...)

Thanks guys. I will do my resets via pulling the batteries (or a battery). In fact, I just put in new batteries.

I like flavors.

Anyways, will we be seeing any coding in TI BASIC from you?

Not true. There is no "Plus" in the name of that calc, it's just "TI-84 Pocket.fr".