Do I have a major problem with my computer. When I press the start button, quite often it will not fire up.?

I have a desktop and I shut down the computer most times when I am not home, or at nights, and the first couple of times I thought it was just 'one of those things', but now it seems to have become a recurring problem. I need to reach over the back and turn off the switch back there, leave for a minute... show more I have a desktop and I shut down the computer most times when I am not home, or at nights, and the first couple of times I thought it was just 'one of those things', but now it seems to have become a recurring problem.
I need to reach over the back and turn off the switch back there, leave for a minute perhaps and try again.

It doesn't appear to be a power problem as it is on the same circuit as the monitor and as I press the button all 3 lights on the keyboard will glow briefly.

Sometimes I need to repeat the switching at the back several times.

I don't really want to leave it on continually.

Thanks for any help you can offer, or any links I can read up on.
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