The guy at the repair shop recommended that I get onto eBay or something and see if I could find somebody selling the same model computer and just switch my HD and new RAM over to it. Remarkably, I found exactly one seller with my particular eMachines computer up for sale, with an auction that was ending this evening. The machine was listed "as is", with the only notation being that it did not come with a hard drive, and I'd emailed the seller to check to see if there were any other issues, and the only thing he noted was that there were some problems with the audio (given that I nearly never use my computer for music, I figured that the worst that brought me was eventually having to shell out another twenty bucks to add a sound card). Also, from the description, it appears that the one for sale has a functioning CD-RW drive (mine had died a year or so back), so I was getting a replacement for that as well. As it turns out, the eBay unit and mine were a pretty good match, since it was missing the HD and the DVD drive (both of which worked fine on mine), but had a working motherboard and CD-RW drive. Throw in the gig of RAM, the video card, and the 350w PS (that I've bought for mine over the past month or so), and I should be good-to-go.
Now, I'd watched this for a few hours, waiting for the seller to respond to my query, and (after hearing back that the system was functional) got a bid in with 20 minutes to go, and at that point I was "winning" with a $24 bid. I was the fifth bidder on this, so figured that I might have some counter-bids to deal with and readied a "bid again" page with my absolute maximum (I was willing to go $100 for the combined cost and shipping). With about 2 minutes to go the guy I'd out-bid came over the top of me, followed in quick succession with bids from what I have to assume were bots. I punched in my max bid (almost twice what the current high was) with 35 seconds to go and had the bots hit again up to about 7 seconds to go, and ended "winning" the computer for a mere $36.00 (plus a fairly hefty $35 in shipping)!
If everything works out the way I'm hoping it will, $71.00 ain't bad for getting this fixed (especially replacing my busted CD-RW drive on top of it all). I just hope that the seller's feedback regarding quick shipping will apply here, as I really would like to get back into my files (and e-mail, etc., etc., etc.) as soon as possible!