The square thing with 4 leads is a bridge rectifier. It's basically just 4 diodes configured so that when AC goes in 2 of the leads then the other 2 are positive and negative. Essentially flipping the negative part of the AC sine wave positive. So you get a series of positive "bumps". It's not DC yet but it's all positive voltage. The big capacitor after the rectifier smooths this signal out. It's still ripply at the top but the voltage never drops below what the regulator needs.

If one of the diodes shorts out or opens up, then it can cause problems for the rest of the power supply.

I don't know if this is your issue or not but definitely something to check out. You'd have to test the rectifier. I do know regulator diodes can go bad though. I fixed a DVD with a similar issue once, only there was a fuse to blow so no strange voltage issues. After narrowing down the problem it was a quick fix.