Well, that's good sign that it boots! It wouldn't get very far if the FRAM wasn't performing its duty as the system's SRAM, at least partially. Even though garbage is being displayed, does it respond to any controls? Can you talk to it via GPIB? Is anything working?
I asked about the LEDs because there are some low-level checks performed at boot on the various buses, SRAM, ROM, etc., and results are displayed on the LEDs. If the FRAM wasn't working right, the unit should fail the SRAM tests (at a minimum) and the LEDs may provide clues. See page 632 in the Assembly Repair Manual for detail on the LEDs. If you don't have the LEDs populated, maybe just run down the pads with a pair of probes attached to an LED.
"Characters stored in the RAM"? No, not that I'm aware. Maybe the FRAM card is interfering with the video controller bus access? Or interfering with a region of EPROM where the characters are stored? The video controller has a DMA controller in it, but HP is not using it in these units. It's all memory mapped I/O for the processor to talk to the video controller.
There is an initialization procedure in the Assembly Repair Manual on page 204. Even if you can manage to navigate through it, I don't think it's going to resolve the garbage.
If the battery dies, yes, the calibration constants are gone, which are the most important thing. You're also going to lose DLP's, stored setups, traces, variables, video setup, display units, serial number, and possibly the model number.
For the calibration constants, Tom over on HPAK io.groups has developed a GPIB utility to restore them using the output from "CAL DUMP":
https://groups.io/g/HP-Agilent-Keysight-equipment/message/149983If you manage to get control of the unit, you could grab a "CAL DUMP" snapshot from your old SRAM and restore them to the new FRAM after doing the initialization procedure.