You may try to connect the monitor to the KVM via DVI-I/A to VGA adapter, then the KVM will work in analog mode even with modern cards, not only with Voodoo.
But why your KVM does not working with any kinds of input signals? Probably it is a simple "switchboard" which simply changes electrical connection between the output and inputs throught a large mechanical switch or a set of simple singal switching ICs (at least, low-cost KVMs are made so).
If using of analog signal is strongly impossible at all, you may search for VGA to HDMI converter, then a HDMI to DVI-D converter. And this, as it is called in Russia, kolkhoz (something made in countryside from crutches and shit because there are no other ways to get the device working) should work with any only-DVI-D device, including the KVM. But it will be a large thing, requiring external power and might have issues with non-HDMI-compatible resolutions like 640x480 or text mode. Reconfiguring all devices to analog mode will be a better way to get all working.
2×Soviet ZX-Speccy, 1×MacIIsi, 1×086, 1×286, 2×386DX, 1×386SX, 2×486, 1×P54C, 7×P55C, 6×Slot1, 4×S370, 1×SlotA, 2×S462, ∞×Modern.