Update: trying the ideas above didn't solve the problem. I read what you mentioned about wiping the drive with the Diskpart command, but since I have KillDisk Pro, I thought I would try that. Since I didn't want to make a bootable DVD of KillDisk and be without my computer for hours (it took 29 hours), I took the drive, connected it to my SATA to USB adapter and ran the Windows version of KillDisk Pro and did a US DoD 5220.22-M erase of the drive.
The result? No BootMGR is Missing message, although during one of the reboots, it came up with "reboot and select boot device or insert boot media in selected boot device and press a key." I ran Windows 7 startup repair from the bootable DVD, and when it got to the part where it said "searching for Windows installations," it couldn't find any and said unknown OS. I ran a fix from the DVD. It said that if it was successful, the computer would restart and Windows would boot normally. Windows then booted normally, and when I ran the startup repair again just to double-check, it found my installation of Windows 7.
From what I've read, this "reboot and select boot device or insert boot media in selected boot device and press a key" message can occur if, during reboot, something as simple as a USB stick is connected to the computer. Is this true? Just to be on the safe side, I'm going to KillDisk the drive again (this time using a single pass of zeros), reinstall Windows and all my programs and settings, and make sure during all reboots that no other storage devices are connected to the computer.