Is it legal to download images from Google for just storing them (no commercial use and no distribution)? I just want to save back up copies of an image I found onto multiple hard drives and have no intention to profit or distribute the files. Is what I am describing legal?
Yes and no. Some image have permission, some do not (one can infer from this Google page). Here is another Google page that talks about how you can find out, for a particular image. This non-Google site is more willing to give a direct answer: "You cannot download or use images from Google without seeking permission from the copyright holder, unless your use falls within one of the exceptions or the work is distributed under an open licence such as Creative Commons".
There is a legal alternative, an archive copy AKA the Wayback Machine (that is what archive.org is about). Its function is to save a copy of web pages that might become unavailable for some reason. 17 USC 108 allows the Internet Archive to make copies, but this is only available to non-profits (not Google), and the archive has to be publicly accessible (not for just personal use).