The Short Version: I fixed the problem by running the “Repair Disk” option in Disk Utility.
I attempted to boot into Windows 7 (Boot Camp partition) but it failed. Instead, the system restarted back into OS X. I knew I had a working partition and had used it recently. Rather than search for tips I went straight into Disk Utility in OS X, clicked on my primary hard drive, and selected “Repair Disk”.
The process only took a moment and in the report it showed that the Windows boot.ini file was updated.
I started the Windows partition back up and this time it worked.