dumpe2fs -h /your/root/partition|grep created
The command will show when the filesystem was created initially, but if we ask for the / or /boot fs information, then this should be the install date.
E.g.:
sudo dumpe2fs -h /dev/sda2|grep created dumpe2fs 1.41.12 (17-May-2010) Filesystem created: Thu Dec 9 21:34:06 2010
Voila!