NICE!  I have one too and love it!  Those are quieter than the rest because they have a layer of Styrofoam insulation under the dome.  And that is indeed the original cord.  I think that model has the updated D3 motor in it too, which means its a little easier to service.  Congratulations!

You can remove the motor from the body of the vacuum and then disassemble the motor itself.  If the spider is dirty, then the fans will be dirty as well.  That is a thru-flow motor.  The fans are on top of the motor and suck the air through motor before discharging it.  So it will be good to clean the whole motor (housing, motor field, etc.).  The bottom bearing is most likely rusty too because it is closest to the water.  That bottom bearing is no longer available through Rainbow.  However, you can still get one from bearing suppliers.  I've found them on Ebay.  Let me know if you decide to take it apart.  I can help walk you through it.  I've posted a few photos just to help you visualize what it looks like. 

The moral to the story is always remove the separator from the vacuum when finished and NEVER leave the vacuum on the water basin when not in use.  The bearings get hot and draw moisture that causes premature rusting. 

After I've disassembled it all, I wash everything in hot soapy water.  I then put the fans in the dishwasher too. 

Your first step will be to remove the motor from its housing.  To do that, you'll need to remove the foam gasket that surrounds the spider.  It's glued on.  Sometimes, it's easily removed.  But you may need to scrape it off or even use some acetone to expose the screws underneath.  Once that's removed, you'll see 8 screws that hold a flange onto the motor support ring (the black rubber ring).  Be careful in removing those screws, lest you strip the screw heads out.  Be sure to use the correct size Phillips head screwdriver.  I would recommend using an impact driver first.  You may also need to scrape out dirt and adhesive in order to get the screwdriver well seated into the screw.  If they're rusty, a little penetrating oil helps.  Anyway, once the screws are removed, you can then remove the flange and then the motor will lift right out.  With the motor completely out of its housing, you'll then be able to take the motor apart.  I always like to remove the fan staging first.  Simply pop the clips off with a flat blade screw driver.  Then use an 11/16" wrench to remove the top fan nut.  It will most likely be easier to remove than the lower nut.  You can use the lower nut as a backup.  They spin in opposite directions.  Once that nut is off, you can then remove the top spacer.  With that removed, take a thin flat blade screwdriver and hammer and gently tap around the edge of the top fan stage.  They will usually all come off together.  If that happens, you'll see the fans and the other spacers clanging around inside.  At that point, you can usually just pull then apart with a little effort.  I always soak the fans in water and laundry detergent and then use a bottle brush to scrub between the fan blades and the blades of the stage housings.  I then run them in the dishwasher. 

To remove the bottom nut, you may need some penetrating oil and patience.  You'll notice that the bottom of the armature shaft is slotted.  You can insert a flat blade screwdriver into those slots for backup when removing the large separator nut.  Once that's off, you'll see the bearing shield that's held on by four screws.  If you want to clean things thoroughly, you'll want to completely disassemble the motor.  That will require removing the lower bearing.  To do that, you'll have to tap it out from inside after you've removed the armature.  I wash everything in the dishwasher (except for bearings and carbon brushes).  You'll also find inside the motor that there's a bakelite air guide.  Remove it and wipe it off but don't throw it in the dishwasher.  Be careful with it, because those aren't made anymore.  Because that motor is a thru-flow motor, the inside can get filthy.  That's why I would completely disassemble everything and wash it.  The motor field will be pretty rusty too.  After washing it in the dishwasher, you might want to take a wire brush to it get the rust off.  Also, if that motor flange is pretty rusty, you might want to buy a new one.  You can get one on Ebay.  That's a part that was used all the way through the D4.  If it's ok, you can use some acetone the get the old adhesive off the flange and the flange screws.  You can get a new gasket off Ebay too.  To attach it, I just use automotive weatherstripping adhesive from Walmart.  I hope this helps!  Don't hesitate to ask questions.  Also, that lower water pan gasket should be the only one you'll need.  You can install a cork gasket between the bearing plate and the motor housing, but I don't think that gasket was spec'd for the D2 motor.  It didn't show up until the D3.  Let me know if you need more photos too!  One more thing:  If you remove that lower bearing, be sure to tap on it around the outside race.  Do the same when reinstalling it. 

This procedure may not be complete since I'm doing it from memory!  LOL!

The universal number for the lower bearing is 88502.  If you do a google search with "bearing 88502", you should find what you need.  Here's a link to another Ebay seller for that bearing.  The top bearing is a proprietary item with the bearing already installed in a mounting plate.  The bearing plate you'll need has four vents cut into the plate around the bearing. 

This is how the bottom of the motor looks with the spider removed.  What you're looking at is the bearing retainer. 

This is the inside of the motor housing.  Note all the dirt and why it would be good to clean it.  This should stay clean if the vacuum is properly used and cared for!