First, I'd say it's worth getting a chainstay protector. Black electrical tape works very well for this, and you can take it off and clean the residue with no loss later if you want to.
It sounds like the freehub (which is what I assume you have on your LeMond; freewheels haven't come on nice bikes for almost 20 years now) has its bearings gummed up. These are the bearings that are turning when you pedal backwards or coast while riding. You can replace the freehub body (new ones are around $20-25 for good quality, 8/9/10-speed compatible bodies) or try removing the freehub body and flushing it with thin grease (e.g., ProLink chain lube) and then putting some thicker oil (e.g., Phil Tenacious Oil) in there.
It's also possible that whatever is inhibiting the freehub from turning isn't internal to the freehub, but rather dirt/grease/grit buildup on the outside, on the interface between the hub and freehub body. This is less likely, but possible.
In any case, you'll have to remove the cassette (for which you need a lockring tool and a chain whip) to inspect well. If you want to remove the freehub body itself, for servicing or replacement, you'll need to remove the axle from the hub, and then use a 10mm allen wrench to loosen the bolt that holds the freehub body to the body of the hub itself. This is assuming the hub is a Shimano. I don't have experience removing Campy freehub bodies, and sometimes sealed-cartridge bearing hubs (from Campy or others) can be screwy to work with.