I'm wondering if maybe the CPU is technically good, but something is causing it to either constantly reset, or never reset. Normally, when the 65x02 is powered up, it is in a state where it needs a reset, hence the autostart operation on the Apple IIe. The autostart involves pulling the reset pin low, then quickly pulling it back up to complete the reset cycle. If you had a logic probe, you would be able to monitor the state of the reset pin, and see if it actually does reset upon power up.
If the CPU reset pin 40 is constantly low after power on, it may cause the CPU to have a non-operational effect, although this would normally show text garbage and not the bars. Which leads me to think the other possibility which is if something is interfering with the reset circuit. Have you tried CTRL-RESET, and if so does it have an effect on the display?