Probably a dumb question, since I'm all for resurrecting old Amiga hardware, but are you particularly fond of this 4.4 board? IMHO Rev. 6 and later boards are a much better design. You can see more about the differences here:
http://amiga.resource.cx/mod/a2000.htmlAssuming everything else works (drives, etc.), maybe swap in a different board to ease your headache? Probably a bad idea though, since 2000's are tanks, and almost always can be fixed.

Your testing process seems sound. Off-hand I think you should still get an "Insert Workbench" screen, even if no floppy attached, but I would hook up a floppy drive in any case, just to see if it spins. If the drive spins and it acts like it's trying to boot then your problem may be somewhere in the video output. If it doesn't even try to access the disk, your problem is at a lower level.
I did a little poking around and maybe this guide might be helpful to you?
http://home.arcor.de/kickstart/TKA/Tutorials/troubleshooter/trouble1.htmlhttp://home.arcor.de/kickstart/TKA/Tutorials/troubleshooter/trouble2.htmlIt's a bit old, but the second link in particular, lists some components that might be checked.
---I wish I was in Austin! Was supposed to go down there for a tech conference last summer, but had to cancel because my workload was too high. HR tells me I have 296 hours of vacation time at my main job and I can't take a bit of it because of too much work. Darn Americans and our workaholic tendencies.
