One of my IIc has the same problem, a couple of @ on the screen, My IIc also wont boot off a working Disk etc.
Obviously whats happening is the corrupted bytes appear throughout the memory map (not just the screen), so when ProDOS loads into RAM its corrupted and crashed, the loading problem is not your Drive or Disk its Bad RAM.
I haven't opened it yet (on projects to-do one day list) just fixed a IIc monitor, what a nightmare, took two hours to re-assemble (44 screws !), its now working again.
My monitor blew the A/C filter caps (then the fuse) hardest thing ever to take apart to get to the circuit board !
Cool little Apples those IIc
one of those brief case computers with the carry handle
will get my IIc out and try the dianostic's test, wont be till next week when I can get to it.
I thought the dianostic test just keeps cycling for ages ? and stops after a random number of cycles