Laptop won't wake from sleep

I have a laptop running Ultimate 32-bit, 4GB ram, and anytime I close the lid
(either plugged in or on battery) when I open the lid all I get is a blank
screen. I have to resort to a "hard reboot". My settings are set to sleep on
lid close. I thought the whole purpose of sleep was so that the computer will
start up quickly upon resuming work. I've changed power settings so that it
doesn't sleep, but when I put it in my bag to go home for the day nothing
shuts down and the computer overheats. I believe I've had the same not waking
issues when in hibernation mode as well, but not sure.
Any solutions?