Took it to the Apple Store today. They replaced the camera for free in store since the iPhone qualified for the free iSight camera replacement program.
Since they opened it for the repair, touchscreen has been perfect (don't want to talk too soon though). It would become unresponsive as soon as the phone went in standby for a few minutes, but I left the phone untouched for a couple of hours and when I went to wake the phone up, touchscreen was responsive as it should. Even when I was taking it home and leaving it unused for a while, it was working fine.
Maybe it was just a matter of reseating the screen connectors.