I had the same issue today on iMac 5K 27" with a fusion drive. A previous installation of macOS Mojave 10.14 Beta 4 apparently messed up the main partition. The recovery partition seemed to be OK, because it enable me to retart the computer and do a restore from a Time Machine backup with a Mojave Beta 3 installation.
The second try for installing Beta 4, it went somewhat better but it got stuck at the beginning of the installation process. Two hints gave me the idea that something was not right: 1) my Time Machine drive had its lights off even though it was connected to the computer, ehich is not normal at all; and 2) there was no prevision how long the installation would take.
Solution: I did a hard restart using the power button and pressed Command + R. I thought the computer would restart on the recovery partition, but apparently it was smart enought to detect that an installation on the main partition got stuck and instead restarted the installation process on the main partition. After that, everything went smoothly.