I think the memory profiler may have got confused over which app pool it should be using (its using a .net 4 app pool).
I'm quite confident this is related to changes in the config files.
If you want things to "just work" again- I'd recommend starting from zero - its usually far quicker than full debugging- we can always do this later if, indeed, it ever arises again (plenty of things seem to sort themselves out on fresh deployments, in my experience). So deploy a fresh install of AMP on a different machine, make sure the web site is 100% working before profiling and retry profiling multiple times without changing anything. If it happens again- try and document the exact step that happened immediately before it not working. This will vastly reduce the time it takes to solve exactly why its happening. It could be several factors- as I say, I suspect the config files, but it could also be errant environment variable, file permissions and a few other things that would take a long time to trouble-shoot.