You should be able to find the trigger switch on the cabinet or in the owner's manual.  Due to it's design, I can't just say tape it down.

There's 3 wires going to it.  So I can't just say splice 2 wires together.  That wouldn't be recommended by Dell anyway.

It may be that you won't be able to defeat it.

Important:  This is EDITED from my original post.  I had a different intrusion switch in mind when I first typed this.

Careful not to do anything with the MB while the PC is powered on and plugged in.  The same for that intrusion switch.  Unit will not operate with intrusion switch disconnected.

Precision 5820 Owner's Manual 

Apologies for the bump, but I just fixed this issue on my Precision 7920 workstation and thought I'd share in case anyone else was searching. There is a three pin connector on the motherboard that goes to the door switch. The red wire is only shorted when either side panel is open, and the system will only boot when ONLY the two black pins are shorted.
You have two options.

1. De-pin the red wire so that the two black connectors that are shorted together are the only two pins connected. Might be wise to wrap this de-pinned wire in electrical tape to prevent shorting on something it shouldn't touch.

2. Unplug the connector, and use a female to female jumper wire in pins 2-3, where the two black pins on the connector are.