Computer fails to turn off

This has been intermittent for some time now. It seems to be more persistent these days, though. When I shut down the system through Windows, it goes through a shutdown routine, then after a few seconds the monitors go black but the computer continues to run. To restart it I have to turn off the main power switch, then turn it back on. Windows loads normally after doing this.

I discovered yesterday, that when this happens one of the two RAM modules stays lit up all the way. It's a Corsair RAM with green, orange and red lights covering the length of it. One module has just some of the green lights on, steady. The other module has ALL lights on constantly until I shut off power.

This is an Asus P5B-E board. Since this problem seems to come and go, I'm thinking it is some sort of connection or other mechanical problem. I don't really know much about anything, though, so I'm asking for other opinions.

Any ideas as to where I should look to resolve this?

I've never been one to do bios updates without a reason, but this may be a good reason. Good idea. I may give it a try.