Since you did not back up your MBR (only the partitions) we have nothing to restore and recover from the situation. Possible fault lies on the MBRrecord or just in your grub config record, things might have changed along partitions since the back up. Arch uses legacy grub (right?) Grub1 or Legacy Grub, so it is a very easy edit on the /boot/grub/menu.lst file.
But the shortest and surest way is to reinstall your grub in the Arch system and then install-grub into the MBR. After installing grub, you will only edit the 'manu.lst' file to boot into your Windows 7. If you need a guide in configuring the grub here is a very good tutorial
. This will sure solve your problem.