Any projector issues, other then replacement lamps, and maybe a fan, are going to be tough to diagnose and fix. Most likely, this issue is related to the main board and the video processing going bad. But, there is no way to know for sure. I don't do projector repairs, but I've heard enough stories over the years to help dial in some possible causes.

The main processing being the issue makes sense, as that likely is after the portion that passes video into your second projector.

I will ask if you've tried other inputs on the projector like the DVI input? That may be an option if only a certain input has gone bad.

A real headache in churches, schools, and other places is that they don't budget for replacement AV and it is always something of a shock when a 'must use' item suddenly fails. So, be aware that certain portions of a AV chain in any facility should budget appropriately for about a 7-year maximum replacement plan. If it lasts longer, great, but if not, at least it doesn't hurt as much.

All this said, if you have no budget for a proper replacement, then I might look for a used model in good working order. The 6,500 lumen brightness is a big perk of this model as were the interchangeable lenses that allow you to place it almost wherever you wanted if you had the right lens for it.

If you can't afford a brand new replacement, then I might go the eBay route and pick up a exact replacement. Be aware that this was made by Sanyo (I believe) and marketed by several companies.
Sanyo PLC-XP100L
Christie LX650
Canon LV-7585

All three of those models are identical to the Eiki.

And, while the Eiki doesn't have many units on eBay, Sanyo has a few more and for less money...
https://www.ebay.com/itm/284678500325