The passage below is verbatim from the Rigol technician:
"After I replaced the fused (250V 250mA S) on the AC input, the instrument booted fine. I tested DC voltage fine. I checked the 250V 10A F fuse for the current channel before doing a DC current measurement, it had a 250V 250mA S in it. I replaced it with the proper fuse and tested DC current usccessfully. I am not sure if the fuse mismatch was the root cause of the AC fuse blowing but the instrument is functioning without any issue."
Apparently, there was this problem of a fuse mismatch. I never messed with the fuses except, after it died on me the second time, I replaced the fuse on the back of the unit with one of the fuses they sent me. Of course, nothing happened--it was still a dead multimeter. I'm worried about any damage that might have been caused by the mismatched fuse, how did this originate in the first place, and why wasn't caught when I sent it back the first time. And what gets my goat is that he's not sure he's found the "root cause"; hence, we don't know if the problem has been or will ever be solved. I can't but help think that I should have listened to the other bloggers who advised buying a plain ol' handheld and not craved for this unit's data logging and data transmission-to-computer features. As Trump once wrote, "sometimes less is more".