Did you try powering the computer up with nothing in the slots? Reason I ask, I once had a very similar issue with my original //e. Computer had a Saturn Systems RAM card installed, which had two chips on it blow right after a thunderstorm (powered the computer up, saw lightning outdoors, shut it off immediately). Later that night, after the storm passed, I powered up the computer, only to see the garbled characters you have on your //e's screen. Popped the lid and pulled one card at a time. Removing the Epson APL interface didn't change anything. So, tried the Saturn card. Still no difference. Pulled the disk ][ controller. Still had issues. Finally pulled all three, leaving the 80 column card in place. Hit the power switch and was greeted with the beep and "Apple ][" at the top, then the cursor just below. Shut it down, then started reinserting the cards one by one. Both the Saturn card and the disk ][ card caused video issues and no startup beep. The 74LS05 on the controller card had blown, and, on the Saturn card, the 74LS266N and another chip just above it blew.
If the computer does this without any cards in place, then it'd be RAM, ROM, or maybe an iffy 6502.
-J