Well, I changed the battery and it worked. I pulled the tabs off the old battery with the protection circuit and I soldered those to the new battery. Voila, working battery. Drained the new battery and recharged it. Everything seems good. I'm running it out now to see what kind of life I'm getting out of the new battery time-wise, just to make sure that I didn't adversely affect it by heat with the solder. Probably not though, as I prepped the battery and made sure that I used the most minimal amount of time to solder (you know, like 3 seconds). Simple. Just make sure that you don't harm that PCB with the 3 wires, because I don't know where to find that if you damage that. Anyone know that bit of information, that would be helpful.
My question now is that there are 18650 batteries that are 3.7 volt that have way more Mah than the one Pono provided (2800). The one I put in was 3000mah. There are some that are 6000mah. I noticed that even though the front screen when charging (that big plug thing) turned solidly green, when I booted the Pono, the green line on the charging indicator while playing had a small block of grey (which usually indicates a not completely fully charged battery). I'm wondering if the PCB is programmed only for the 2800mah capacity. I should have bought the 6000mah just to see if that were the case because I won't readily be able to tell with the 3000mah because it is so close to 2800mah.