Huh not sure to understand everything you said:
and the second time we tried the windows 7 disc it gave us the message "BOOTMGR is missing."
Did you meant that AFTER the install it showed that error message? Cause that makes no sense since you just installed Windows and it should have installed the bootmgr by itself. The only thing that I can think of is that you messed you actual Windows install, then when you boot your computer it just doesn't read the disk and try to load your old Windows. Do as jsanthara suggested you.
Also it could be your DVD drive that is going bad. It is easier to try another drive than downloading the whole Windows from the internet.
Your Windows 7 DVD might be scratched or partly not readable. Since you have the cdkey for it, you should try to download Windows 7 on the internet and burn the iso on DVD and try to use it instead.
Note that Windows 7 discs doesn't work with every DVD drive. For example my
NEC DVD-RW ND-3550A ATA doesn't recognize it at all. I had to use my cousin's drive to make backup of my Windows discs, knowing that I used 3 different DVD disks brand, so that I will never have that trouble again. ^^ Ok I agree that you don't need to do 3 backups but I prefer being safe than sorry.:-D
Always do a backup of your Windows CD/DVDs so that you don't have to use the real disk to install Windows. That way it won't be exposed to sunlight and won't scratch at all.