Oh crap! I was afraid of that. . .
OK I'm back; and according to the video by the guy from parts-are-us or something like that, (Point of interest, if you do a Goggle search on 'Roper washing machine springy thingy replacement' it actually works!!) this should be a fairly simple fix. (Oh damn, I never should have said that. . .)
First step is to remove the two screws on either side of that console that's sticking up there at the back of the washer. The screws are tucked away at the back below the red arrows.
Then pull the console towards you a half inch and tilt it back out of the way then unplug the door switch connector there at the end of the arrow.
When I tilted the console back I discovered an electrical/operational-sequence drawing folded up and tucked neatly away back there. Now that might not get you all a twitter but as an old electronics guy (And when I say old I mean the first thing the military trained me on was vacuum tubes. If you don't know what those are then you've never had the joy of owning a real radio that that took up a whole cabinet by itself or a15" black and white TV that weighed over 50 lbs. and you've never had the enlightening experience of getting zapped by the couple thousand volts at the cathode end of a hot vacuum tube, and I feel sorry for you. OK, looking at the little pinpoint greyish scars on my fingertips from getting zapped by miniature lightning bolts, maybe it's myself I feel sorry for. . .)
Anyway, as an old electronics guy finding diagrams like this is better than se---, better than chocolate icecre---, well at least better than a stick in the eye.
Now back to the task at hand.
Take a screw driver and pop loose the two clips that used to be here on either side, (In case you didn't get it, this is the part where you look at the red arrow in the photo above.) then go fetch your long grabby thing and retrieve the clip you managed to drop down there into the no-man's land behind the washer,
then grab the main cover, brace your foot against the bottom edge, tilt it towards you 30 or 40 degrees and lift it off.
When you finish setting the main cover aside and turn back to the washer you'll have a moment of horror at the crud that's collected in and around the thing over the past 12 or so years, so brace yourself.
Just like the guy on the video said, the errant spring belongs near the back left corner and goes from the bottom of the tub down to the frame. Also just like the guy from the video said, (I don't know his name but let's call him Bob from now on; it's shorter.) the hole in the frame may have rusted through, releasing the springy thingy in the first place, in that case it's OK to just use a nearby hole in a less rusted part of the frame.
Getting down on the ground, figuring out where the two ends of the spring belong and getting it back in place should take all of 15 or 20 seconds, but when you have to get back up again, go fetch some pliers to stretch the spring with, get back down on the floor, re-orient yourself to all the holes again, and then finally put the spring back; well - it takes a little longer.
Before following Bob's instructions on closing everything back up again, I took the time to do a bit of spring cleaning and got that ring around the top of the tub as well as that plastic spout that dumps water into the tub (That grimiesh colored thing at the top of the big rust stain down the washer's back panel.) cleaned up a bit. Not clean mind you, I think that would take a trip to the store and the purchase of a new washer, but I did get it cleaned up a bit.
Even though Bob made it look easy I was expecting an epic wrestling match to ensue as I tried to get the main cover to fit back on the washer, but Bob was right all along, it just slipped right on.
Then it was a simple matter of re-installing the two clips that hold the back of the machine to the cover, flipping the console back over and screwing it down, running a short test, removing the console screws again, flipping the console back, plugging the door switch cable back into place so the thing will drain and spin, flipping the console back into place, almost screwing it down again before realizing I hadn't tucked that really great wiring diagram back where I found it, flipping it - well - you know- finally screwing the console down one last time and; wa-la! It works!
Of course no job should go too smoothly. If that happens you start to expect it every time and we all know that's not real life so it would just be setting us up for disappointment later on. (At least that's what I tell myself.) So to finish up this job with the proper degree of calamity, I narrowly averted a minor disaster by remembering, just in time, that in order to pull the washer out from the wall I have to remove the lid from the lint filter we have in the drain line. (We have a septic system and there's no way we want all those little bits of indigestible synthetic lint clogging up our drain field one day!) Since the drain line from the washer goes into the top of the lid that I had temporarily forgotten about and just left dangling, I almost dumped the contents of the washer down behind the drier!
But in the end I got all the bits back where they belong and the test cycle ran flawlessly. Now when the washer goes into spin cycle it no longer booms like a demented base drum falling off the stage at a Kiss concert and rolling down the steps, getting faster and louder as it goes!