Trouble bringing up the computer

My Acer Aspire 3680 has began to require (usually) a three-step process to get it to come up after powering it off for the night.

First I turn it on. I hear noise like it's going to come up, but after about 30 seconds, it turns itself off.

Next I press the power button again. This time I see the normal Acer screen, but it's a very dim screen. It then turns totally dark while I continue to hear the hard drive working, but it never comes up. So after about a minute. I press the power button and it turns off.

Finally (third time) I hit the power button again. This time Acer comes up brightly as is normal, and within a few seconds, I am able to log on.

As long as I just lock the keyboard when away from the computer, there are no further problems, but it's when I shut it down, and try to bring it up the next day that the problems begin.

At first, I was told it was because I had an external keyboard and mouse plugged in to USB ports. So I unplugged them. And leaving them unplugged until I brought the computer up worked for awhile, but eventually, it begin to require turning it on/off at least 3 times befure it came up, even though no periferials are plugged in.

This is a mystery to me and somewhat annoying becuase it takes quite a bit of time to get going in the morning. Any light that anyone can shed on this problem will be greatly appreciated.