OK.......I'm back in business!
Here's what THEY did to get me running:
Unplugged EVERYTHING (I thought I had done that by removing my mouse, printer and keyboard) They pulled out the video cards, all four ram modules and the network card......AND the CMOS battery as well as disconnecting my hard drive and CD. They then powered it up and heard the single beep which apparently signifies "Your board's OK, but you need some RAM".
Then they reinstalled a single module of some other known-to-be-good RAM.
Ran a test of the power supply with a little hand-held "Power Supply Checker"
Fired up the machine and actually got BIOS to display.
Then they tried using MY ram, one stick at a time. One of them didn't allow boot and was set aside. The other three did work, singly and as a group.
One by one, the other components were reinstalled. Then the fourth RAM stick was installed again.......and total ram (for some reason) indicated that it was now working. (Peanut butter on the pinouts???
When the drive was reconnected and booted, it came up quite readily and went straight back into the Easeus partitioning program that I'd been trying to run when everything died on me initially. (I explained to the tech I'd been trying to 'carve out' a partition large enough to re-install Windows without reformatting so I could save my data; I also explained that the only option I seemed to have in Easeus was to increase the size of a 100MB partition that already existed. He recoiled in horror (sorta kidding but not really) and said, "That's the SECRET 100mb Microsoft partition that nobody knows the purpose of and NOBODY should play with!!!)
However, we let the re-partitioning continue rather than shut it down.......and it appears to have worked without consequence. (My secret, 100MB Microsoft partition is now 10GB in size......although I no longer have the need to reinstall Win7!) (Wondering now whether I should put that partition back to 100MB?......or leave well enough alone.)
Tech-man also installed my IDE 120GB drive for me using the onboard IDE connector of the Intel board......and booted up again. This time, the computer tried to boot using the IDE, which he quickly aborted, went into BIOS and change the boot order so it would go to the WD primary drive first.
So, at the end of the day (aside from not yet uncovering the mystery of the 'secret MS 100MB partition'), the lesson learned is, when you read "Unseat and re-seat everything........do EVERYTHING!!!) (I had unseated the RAM, but didn't actually pull it ALL THE WAY OUT and sit it on the bench!!)
Thanks again for all your tips/tricks/suggestions and contributions, guys! I'll no doubt be talking to you again.
Michael.