We got some new Dell machines and 3 of them are having similar issues. Computer shuts down then reboots to a white Dell screen detailing the error in a pre-Windows environment.

The first time it happened, I snapped a picture and luckily had the code for Dell to get us a replacement for the computer.
Second time it happened, someone rebooted the computer and we didn’t get a chance to get the code. Same thing happened the third time it happened.
When I contacted Dell about the issue, they wanted the code and when I couldn’t produce them, they said I’d need them but the only help the rep offered was to check the BIOS logs, saying that he doubts they’d be there, but it’d be a good idea to check. Checked and, yeah, they’re not there.
I’ve tried running Dell’s diagnostic tool, SupportAssist, and it gives me an error that it can’t be run. I also tried the online tool from Dell (after supplying the service tag) and it doesn’t move past the first step of diagnosing (left it alone for hours).
The codes don’t appear in Event Viewer. In one of the affected computers, there is no activity between the time it went into this and the time it was rebooted.

The only other option I know of that will work at this time is to wait for the error to pop up again, but based on the first occurrence, that could take 2 weeks and I’m not sure if someone won’t just reboot again, making us wait again.
The codes seem to be unique, something produced by each machine individually as they encounter the issue (it appears that way, anyway), so I don’t think I can reuse the first code for the other two machines. Plus, I’m not entirely sure it is the same error and I’d like to make sure it is the same error.
Is there anything else I can do to get ahold of these codes?
Thanks!