I have an 8116A, which is similar to the 8112A. Here are some ideas that might help.
Although the manual doesn't explicitly say, I'm going to guess the blinking parameter LED, "WID" in your case, is an indication that various settings conflict with each other. For example, setting a width of 100us when the period is 10us. In your power-up photo, a period of 0.00ns I would say qualifies. (The 8116A uses the ERROR indicator in this way but does not blink the parameter LED.)
The settings are stored in battery backed RAM when the unit is off. Because you replaced the RAM and maybe the battery too, the contents of the RAM are now garbage and appear to be creating a nonsense setting. The manual says the firmware is supposed to restore the unit to factory default settings when RAM corruption is detected, but maybe this is not happening and/or the firmware is totally confused.
You can try performing the factory setup manually by pressing STO/RCL and then use the right hand vernier to select "0" if not already displayed. Then press the middle bottom vernier to recall. However...
You also mentioned the front panel buttons are not working except LCL. There's nothing special about LCL. It's in the keyboard scan like all the rest of the buttons, so it's strange it's the only one working. Perhaps there's something mechanically wrong with the keyboard (maybe a cracked PCB or open traces).
What I would try next is to see if the unit can detect button presses at boot. At power on, the processor does a scan to see if any buttons are stuck. You can use this to verify the function of all the buttons. Start with the LCL button. Power off, hold the LCL button, and power on. A "o" should immediately appear in the display. As soon as you release it, the unit should complete the boot sequence.
Now try the same thing on another button, like STO/RCL. In the 8116A, and probably in the 8112A too, as long as you press the next button you want to test before releasing the previous one, the unit will stay in the "o" mode. You can use this to quickly verify all the buttons on the front panel. This should at least help point to either a firmware or a hardware issue for further troubleshooting.
Oh, and if you haven't done so already, make sure all the power rails are in spec.