OK, there is a vent pipe and an electrical conduit running up one side. Have to get down on all fours and look in the bottom of the lower cabinet to see it. It's covered by a panel on the top shelf. Fishing around behind the top cabinet with sheets of paper, it appears there might be a #8 screw at 32" and 10" from the bottom of the cabinet, near the forward edge. I can't find anything on the rear edge. There is a strip of clear silicone on one edge, over the decorative wall trim, but it's not adhering to the wall at all. Until it falls off, I'll leave it be.
Ourtinhouse; since your's has fallen off, you could attach some cleats to the the wall, in a position that would allow you to run screws into them from inside the cabinet. They need to span the distance between the wall and the existing cabinet back. Locate either a stud or install some screw in mollies and attach the cleat to the wall. Seat the the thing in a bed of silicone adhesive, run screws (pan head with washers) from the inside of the cabinet, through the cleats and attach it to the wall.
I hope this makes sense. I can visualize it better than describe it.