HI all. Thanks to the numerous other threads on this topic, I didn't panic when, mid-smoke yesterday, my MES 30 quit. I was able to finish my ribs on my trusty ol' gas Weber (they had some of the better smoke rings of my many efforts - hmmm...).
I drilled out the rivets on the back panel, unscrewed the left and right screws holding the electric burner to the back, interior wall, while leaving the middle screw alone (it's a ground wire, attached from behind with a nut).
When viewed from the back, I found that the left connection had corroded. See first photo. I wound up cleaning it up, then soldering the connection in place. See second photo.
I reattached everything, and used stainless steel #8 x 1/2" screws to reattach the back panel. All seems to work.
I'm currently smoking a 7.5 lb pork butt. Let's hope it keeps a'smokin'!