MikTeX 2.8 has been released recently. Since MikTeX cannot intelligently update over its previous installation, the extra (non-MikTeX) packages I had installed in the older installation need to be imported into the new installation. To do this, first install MikTeX 2.8. And then import the packages from the older installation using this command:
mpm --admin --verbose --repository="C:\Program Files\MiKTeX 2.7" --import-all
Make sure to use the MikTeX 2.8
mpm.exe for this.
For more: MikTeX 2.8 installation page