How do I connect this flat panel screen?

[Ilwrath]

The funny digital connector is a DVI.  ;-)

The monitor should be able to work with either connector, though you may need to set a switch or option on the monitor itself to tell it which input to use.  Also, for the VGA-style connector, you'd need to make sure that you have a resolution/scan frequency within it's acceptable range.

Can you get an on-screen diagnostic menu from the monitor, itself?  Or is the logic board in it fried, perhaps?

[Ilwrath]

so I'm confident that it's a logic board fault.

Yeah, that would be my guess, as you're not getting any on-screen diags, or anything.

As for DVI, I'm not sure if it is scan-rate dependent in any way, or not.  As I understand it, the true digital portion is NOT, but my understanding of it may be confused, as I haven't really dealt with it.  (I do know that many DVI connectors contain an analog fallback, which IS scan-rate dependent, though.  That's how the DVI -> VGA adaptors work...  They don't convert digital to VGA, they just take the analog signal that is also in the DVI and send it to the VGA pins.)