A battery? How would that help? Not doubting you, just honest question. I feel like I'm missing something very important about how smartphones work.

Mmm... it also happened to me with my (now defunct) Galaxy S1. I can't explain it, but at some point its battery developed the "bloated, about to explode" look and the phone worked but it was very slow and crashed frequently. I changed the battery and everything was ok. Later it died of unrelated causes.

I guess the processor wasn't being fed properly in regards to electricity, meaning not executing at the speed it was supposed to or other side effects.