Cannot start computer

Hello,

I have a Windows Vista Home Premium with all updates. Since some days my computer has started having problems when coming out of sleep mode. The fans rotate; power & hard drive LEDs go on for a second then go off. Then all goes quiet for a few seconds and this repeats itself again and again. The only way to start the computer is to keep the power button pressed in for a number of seconds, and then restart the computer. Then it runs normally.
I wonder what's causing this.

Any help would be greatly appreciated.

Thanks.