So the problem appears to be solved. The issue was that on waking from sleep, the laptop would crash. Then, when trying to start it up again, it would not even get as far as the Apple logo screen before failing. The solution to this was to hold the power button until the light flashed and a high picthed noise was heard. I’m not sure what exactly this does, but it made the laptop start up.
After some searching around, I found this article pertaining to sleep modes. I did what it said, and changed my hibernate mode to 0, and now the laptop seems fine. Also, I’ve saved myself a precious 2GB worth of hard drive space, which on only a 70GB drive, is very much worth it! It does mean, however, that I can’t leave it on sleep for long periods of time, since it drains the battery to keep the contents of the RAM happy. I think I can live with that, though.