How to troubleshoot a black screen (no video) on boot?

On a related question to this one, now I have a file server whose power supply and fans spin up, but gets no video and no beep codes.

I have tried two different video cards in the system, and neither one sends any signal to the monitor. The monitor is a known good one; just borrowed it from a working server. The system does not have any hard drives connected to it -- just a power supply, motherboard, CPU, CPU fans, full memory, and the video card.

I've tried the obvious "swap the cards" trick. Are there any other reasons I can troubleshoot for dead video? CMOS? Memory?

A blank screen does not necessarily indicate a broken video card, it could be anything in the pre boot sequence. The fact that you are not getting an CMSO beeps indicates that it is not even POSTing properly, so it could easily be CPU, RAM, Motherboard.

Unfortunately the only way to find out what is wrong is to swap out components and see what works.

Yes.. I don't think there is a better mechanism than "Swap the Cards". However in some cases you gain more ability to troubleshoot when the system is partitioned. As an example I have seen some occasions that the mother boards make beep tones when the PCI cards are removed.

There are some pluggable devices called "Diagnostic cards". The manufacturer claims they can be used to diagnose such issues. I tried one card but not happy with the result. You may find some cheap Chinese stuff here.

Keep removing hardware until you do get a beep.