Glad you got a PC that you love & works well for you.
You can use an inverter but there are issues with doing that, some research in these forums will clarify them, there are plenty of threads discussing it. The best solution is to use one of the Carnetix P/S like the P1900, it will output the 19V you need plus a second 12v output for your monitor. You can add on a 5v regulator as well if needed for USB devices. The P/S & 5V regulator are available here in the MP3car store.