New harddrive on a macbook pro 13 inch, dvd drive doesn't work, what do?
There is a few way you can do this from the working MacBook. The first is to follow the tutorial here which will take you through the process of making a bootable USB disk for Mountain Lion.

The steps involve


Reformat the USB stick to HFS+
Extract the install image from the downloaded installer
Write the image to the USB using Disk Utility


Alternatively just download the Lion DiskMaker software which will do all the work for you.

The only problem I can forsee is that you need an 8GB USB stick for this to work since the OSX installation is bigger then 4GB.