After screen is opposable
?
Those 5100-series monsters have so many issues I don't know where to start. Wait, I do--the power supply board. You have to start there. Sort of...
First, I'd pull all of the modules out except the CPU, isolator and ranging assembly. Inspect them all for burnt traces or blown up things. Then pull the power supply board and inspect it as well for burnt things. If none, then reinstall it and check all of your power supply voltages. If all the voltages are OK and you still get absolutely nothing on the display, then you have a problem somewhere in the CPU, motherboard, display or display clock circuitry. The display clock is actually a 555 on the PSU board, something user
Runco990 discovered after quite a bit of searching. You can find plenty of old EEVBlog threads on the 5100-series.
If you do find burned up PSU sections, you need to check all those tall modules for shorts. The tantalum caps that are sprinkled all over like to develop little black holes that can seemingly sink almost infinite current, burning up traces and PSU components like wildfire. The two on the bottom of the HV module are notorious for this, but there are others.
There are a large number of revision levels for the PSU board as well, so it probably won't match up to your schematics perfectly. There are some zeners used as voltage drops for regulators that like to self-toast, I use new 5W parts and stand them off the board. It's a crappy design, IMO, but if you try redesigning all of the issues out of these you'll be at it for decades, like Fluke was.