Jeff Carver wrote:...Thanks for the clarifying photos, Gordon.
Your are quite welcome.
... on the U4, I've pretty well destroyed the mounting points for several of the connections. I don't know if I used too much heat to desolder or what. ...
Not much heat is required to soften the adhesive that bonds copper foil to the PCB's substrate.
...Is there any recovery from this, or do I need to replace the motherboard now?
It might be salvageable. Here is another image to work from. Its view is shifted down to show more tracks, and some markings have been inserted: The first things to check, visually and with optical magnification, are some of the narrow tracks of copper to ensure they are still connected as needed.
Starting at U4's right, the wide-track through "S" (FET's source pin) branches at its lower end into two narrow tracks. One heads to the right to connect at C86's top terminal; while the other branch heads left and connects to R230's top terminal. If either narrow track is open, it will have to be reconnected (can do by paralleling the broken track with fine Cu wire, soldered at each end). By "fine", I mean small, such as 0.010" to 0.020" diameter. Rip apart some stranded conductors in trashed electrical cables to source such wire. Wire-wrap wire (if you know what that is) would be a good alternate.
U4's "D" (drain pin, at lower edge of its case, has no connections to it -- other than the missing pad and track coming down from the marked "D-tab" pad. Thus, you need only solder the large tab to the large pad. But, I suggest that you first spot-bond the FET's case to the PCB before doing its mounting soldering. Note that with on two soldered connections (S & D-tab) the component would be only weakly (mechanically) attached to the PCB.
At U4's left side, the "G" (gate) pad used to have two narrow tracks fanning out from it. One heads down (under the "Q45" marker to connect to the bottom terminal of R230. A fine wire jumper between the FET's G pin and the resistor will have to be fabricated.
The narrow track, marked "TPvia", is simply a conductor that heads through the PCB, and emerges in the middle of Test-Point #128 (a point that is used during Roomba's mfg process). You may ignore replicating that conductor.
Oh, one other thing: You will be doing more than the usual touching of the FET's gate pin. Due consideration to avoiding electrostatic discharges into / out-of the FET's gate is necessary to prevent killing the device before it gets connected to the PCA copper.
You might google for "ESD safe handling practice", do a bit of reading and see if you can decide how to modify your own device handling procedure to enhance a component's safety. Sorry, it is an overwhelming topic, yet, if the component, and the system it works with are cheap, and no life-support electronics are involved, the tactics can be reduced to safe rate equalization of differing potentials (voltages) between a component's pins and any conductor of electricity they will come close to, or touch.
Good luck Jeff!