Thanks, all, for the replies! I believe the problem with my PC is a hardware problem. The backlight on the screen often turns off suddenly and then won't turn back on unless I restart the computer. Also, the DVD drive is broken.
I will ask the repair shop (factory authorized center for post-warranty repairs) if they need the hard drive or not. If they do, I'll try some of the strategies described above.
I back up all my data files regularly but have never used one of those utilities that replicates an entire hard drive (OS and all). If I wipe my hard drive, even with all my data backed up it is going to be a huge pain to restore the OS and all the programs.
Thanks again!