You can install Windows 7 from a flash drive if your computer supports it. If not, why not replace the optical drive so you have one that works?
If you do not have a Windows 7 installation DVD, you can download a legal copy with SP1 integrated from here: Official Windows 7 SP1 ISO from Digital River
Make sure you get the same version you have, Home Premium, Pro or Ultimate and 32 or 64 bit. Note that Basic or Starter is not available.
You can now use the downloaded .iso file to create a bootable flash drive using Universal USB Installer – Easy as 1 2 3
Simply start it, select Windows 7 from the drop down menu, point to the downloaded .iso and your flash drive, and your off.