Strange effect with Stratix FPGA

Can't you change the unused pins to Input with Weak Pull-Up or Bus Hold? That way you don't have to tie an external resistor. Of course, the light will always be on with a pull-up, but at least you'll know why.

How fast is your shift-register toggling? What kind of data is going thru it? Is it going into a RAM or registers? From your previous post, you had one with a ton of registers through most of the device. If they're all toggling at a fast rate(i.e. a fast clock and constantly changing data), you'll use a lot of power. Having it go into RAM should significantly reduce that since you're only reading/writing a single RAM and incrementing counters. Although the power supply on the demo boards should be fine for almost all designs, if you really get everything toggling at high-rates, I could definitely see that happening. Glad you're making progress though.