1) Navigate to Installer Location (Diablo III-8370 etcetc)
2) You should have Installer tome 3.mpqe and Installer tome 3.mpqe.part
3) Delete the Installer Tome 3.mpqe (should be 0kb) and remove the .part from the other one.
4) Rerun the downloaded - even when it says "Finished Downloading" at the bottom - don't close or hit cancel, let it keep running and wait for it to launch the installer.
5) Install, should work, hopefully :)