Here's the board for the black DT-830D. Unfortunately, it's a DOA. In some modes, a character or two will show up on the display, but in many, it stays blank and there's no sign of life from the added continuity beeper, so I doubt it's just the screen. Soldering is somewhat messy as expected.
Interestingly, the board looks quite different from my others or any I saw online. There's a 358 opamp added, *no* DC trim pot, and the IC (chip on board thing) appears to be installed at an angle, with only 40 pads drawn from it (11-11-10-8). It's also got nice looking "hatched" patterns filling the empty spaces (grounded, I guess). The little daughterboard for the jacks is at a different height and is using three connecting wires as standoffs. Soldering for the wires looks like crap on the mainboard end. There's barely enough to fill the holes and the main V/mA one looks like it may already have broken free. Otherwise, it looks like a sturdier means of holding them. They sit lower than the mainboard, so that the back of the enclosure acts as a stop now when you press on them.
This is the model with the square wave output and continuity features. The diode test appears to share the setting for 2000 ohms. It's also got a battery compartment with spring clips in a unique "reverse polarity" configuration. There's also another unstuffed spot on here by the center hole. As with the other, I have no way to know if there was supposed to be a part there or if it was optional (no labels either). I'm guessing those three pads in the upper right with the 100 ohm resistor are where the trim pot went.
BTW, these pictures are sized and aligned so that if they're in the same location, you should be able to bounce between them with the pads and holes lining up (top layer is mirrored).
Take Care
PS@marshallh- Do you mean they blew up with nothing connected?