Replaced the battery... and it entered and endless loop of "apple symbol for a few minutes", "spinning clock", shutdown, "apple symbol...", and so on. Tried to restore using iTunes, same issue. Then I decided to open it again and check all the connectors... put it back together, new restore... and "voila"! It's working.

It's unfortunate that I had to restore the system... but all is well when it ends well. Just remember to always backup before replacing the battery.