I'm pretty experienced with repairing iPods, and I got this one 16gb nano with a torn clickwheel ribbon (that attaches to the...

My theory is something got damage when it originally got smashed and the screen replacement has triggered the malfunction I would say you are right, I had similar experiences with hot chips and it has to do with shock damage. An iPod touch I had the same problem and it also had a flickering LCD backlight (it would go out randomly and the come back on every 30 mins or so) I ended up taking it apart and took a heatgun to the chip hoping it might reflow the solder a bit. Welp I ended up frying the chip in the process. If I was you I would just be thankful that its working half decent and put up with it. If you go and try to fix it, be prepared for a total loss.