Just thought I'd give an update to those interested.
I got the CPU to finally sit right, so no more flashing power light for me. I also had a chance to check my power supply with a multimeter; at least under no load, it's outputting the correct voltage.
The Denise issues I was having were actually caused by the case. I had noticed that there were a few cracks in the case, some especially large ones in the bottom half of it. If I take out the motherboard from the case and let it simply sit flat on a table (on top of an anti-static mat, of course), it doesn't have any issues. Seems that it's cracked enough to the point where the motherboard bends slightly when put into the case, accentuated by the fact that it's missing half of its screws.
So, guess I'll have to repair the case now. I think I'll try an epoxy repair first, unless there is a better option.