A few steps into the installation, there is a screen showing my hard drive, with
sda3 partitions. But when I click to install with one of them, it cannot find the root file. How can I get past this and install successfully?
It will take you to the advanced partitioner if you select "Do Something Else". You have to specify one of the partitions, tell it to use ext4, to format it, and that it is to be used as root. This will remove any and all data on the partition.
If you select "install alongside" then it will make room on the hard drive to install Ubuntu to by resizing a partition automatically. Some people like to have more control over how Ubuntu gets installed, hence the advanced partitioner.
I suggest you make backups of any important data before proceeding, as if you make a mistake at this point you could stand to lose a great deal of data. Backups are recommend SOP in any case.
Have a look at the community installation guide.