I'm not sure if it's the problem or not - but some PCs have an option in the BIOS to re-POST the video BIOS after waking up from sleep mode. You might try going into the BIOS and turning the option on, if it's there (and turned off). Based on what I've read here, it almost seems like the video board isn't wanting to wake up with the rest of the system. Anyway, on my machine the option is under Advanced Power Management Features in the system BIOS Setup - I believe it's called "POST Video BIOS on Resume". It might not have any effect at all, but it seems like it'd be worth a try.
@computer idiot: Like clifford_cooley says, your PC will only use as much power as it needs. Sleep mode does conserve a lot of power - but only when it's activated. It won't have any effect on your power usage while you're actively using the system. I use sleep mode a lot because the PC comes back up a lot faster than from a full shutdown. Also, with my UPS, my PC will run for days off the UPS if it's just sitting in sleep mode - versus about 30 minutes in full-on mode. So, I've got my system set to automatically enter sleep mode in the event of a power failure, which gives me time to get my generator fired up and stuff, and I don't worry about losing data, or something not saving correctly using a forced shutdown (the other alternative.) Anyway, in most people's cases, you're probably best off doing what others here have recommended - just shut it down when not in use.