Just a quick note to hopefully help someone else out in the future.
I was attempting a fresh install of Yosemite on an old MacBook Pro that hadn’t been turned on or even charged for quite some time.
I couldn’t get past the system eligibility check. It turns out if the system time is off, you can’t connect to Apple’s servers to download the software.
The fix: Click Utilities and Terminal.
Type “date” and press return. You’ll likely see an incorrect date.
To update the date and time, type “date MMDDHHMMYYYY” and return again, substituting the appropriate information in, such as 092416152016 for September 24, 2016 @ 4:15pm.
Quit terminal and try the installation again, you should be able to complete the installation now!