I am trying to setup a 4x40 display. My understanding is that it functions like 2 - 40x2 displays.
That is correct. You should find that it has two enable pins, one for each half of the display.
Using the LiquidCrystal library it uses the 4 bit mode instead of the 8 bit mode.
You can use either the 4-bit mode or the 8-bit mode. The code for the 4-bit mode is a little more complex to write but since you are using a pre-written library there is no reason for you to use the 8-bit mode.
Should I have wired the unused inputs on the display to ground?
This is one of the great mysteries of life but the general consensus is that it is unnecessary.
At present all I get is both halves of the display the upper line is all solid blocks, and the second line is blank.
Do you you have one line of blocks in total or one line for each half of the display? Remember this is equivalent to two stacked 40x2 displays, not two side-by-side 20x4 displays.
A line of blocks means that the display is not properly initialized. This is almost always due to faulty wiring of one sort or another, even on those setups that are allegedly wired "correctly". Also, In order to fully utilize your display you will need to use two instances of the LiquidCrystal library. An easier method would be to look for and implement the LiquidCrystal440 library.
Don