My understanding is that GRUB (using the chainloader command) successfully calls the Windows bootloader when I ask it to run Windows, but I think the Windows bootloader is corrupted. It is corrupted to the point that I cannot even use the recovery disk or install disk to fix the system.

I think a Windows update broke it. I have OS probing enabled, and it successfully detected (and booted into) the Windows partition back when I first installed Debian. It still detects the Windows partition, but Windows bluescreens with an error message that I can't remember off the top of my head, but both Microsoft's support forum and other resources basically indicated could only be fixed with a reinstall. Debian, of course, boots just fine.

I ran chkdsk on the Windows partition with the Windows Recovery Disk and I also checked the partition in Gparted, and both processes found no errors. The Windows partition is perfectly readable from Debian.

So I'm inclined to believe that Windows broke itself.