Weird battery problems

I have had my international unlocked M7 for almost 2½ years now. For the past 6 months or so I have had weird battery problems.

When on the lower half of the percentage, i.e. below 50%, sometimes it drops incredibly fast, and the phone just dies. At times it goes from 30% to nothing for instance. When I add the charger it lists the battery as 2-5% or something.

Nothing gets hot, and I have tried to use the saver functionality. I don't think there are any apps that cause this, I have tried to keep an eye on it.

I have also tried GSAM, but it didn't tell me anything new - I can install it again and post some logs, if that would be helpful.

What I have done:
* Recently I went to a shop and had the battery replaced, since I assumed this was the problem (battery getting old), but it didn't changed anything. There is, of course, a remote chance that the shop screwed up and didn't replace the battery and screwed me - I have no way of telling...
* I have also recently rooted/unlocked/wiped all caches and installed a ROM from here (Eragon), but that didn't change anything either...

My only conclusion is that this must be a hardware problem - am I correct in assuming that?

Any help/tips are welcome!

Thanks!