Powering high-power laptop from DC without inverter
In theory, you should be able to use a simple DC-DC converter to generate the 19.5 Vdc from your 12V battery bank.  

Where you may run into problems is that many Dell computers have a 3rd conductor in the DC power cable that allows the computer to determine what size of power supply is connected.  It does this so that it can throttle back the current consumption if a too-small power supply is connected.

On all of the Dell laptops and power supplies that I have worked on, the mechanism is a Dallas One-Wire memory chip inside the power supply.  This connects to the laptop via a 3rd conductor in the power cable and connector.

You can usually see this by examining the plug that goes into the laptop.  The plugs with the 3 conductors are a coaxial plug with a shell on both the outside and inside of the large-diameter barrel and a quite-small center pin in the middle of the plug.  That center pin is the data line and the two shells are the DC power connections.

The easiest way to do what you want to do is to obtain another power supply and scavenge the DC power cable that feeds the laptop as well as the One-Wire chip from inside the power supply.

There is a plethora of DC-DC up-converters available with the power requirements that you require.  Amazon or Digikey or even eBay will sell you something appropriate.

If you are finding it difficult to obtain a donor power supply to scavenge parts from, you can use your existing power supply.  Simply splice directly into the laptop power cable coming out of the power supply.  There would be three conductors: two large conductors for DC+ &amp; DC- as well as a much smaller conductor for the data line.  Simply splice into the two DC lines and you will be good to go.  Be sure not to cut or short the data line.