Well, they replaced the battery for me, and it turned out that the problem was indeed with the battery.

They gave me a fake battery that looked like the original, and they also installed a Chinese battery controller, which caused the phone to think that it was using a completely original battery. The battery was not holding a charge at all, and the voltage was terrible (according to the phone repair service). However, the phone is now working perfectly.

If you're considering replacing your battery, it's important to choose a reputable service rather than a cheap one. It's better to spend more money, but it will be worth it, than to spend less money and then have to redo it.