A Clean Coin Question.

1. By a lot. It has to be a pretty scarce coin for it to retain much of its value after a harsh cleaning, and dremelling is about as harsh as you can get. It sounds like your coin has been "whizzed".

The price of a coin is a function of supply and demand, and cleaning makes the "demand" side of the equation fall to near zero - collectors just don't want badly cleaned coins. On the supply side, part of the reason that uncleaned, pristine old coins are worth more is because relatively few old coins are still in that pristine, uncleaned state.

2. Not really, no. There are ways to try to disguise the damage, known as "artificial toning", but there's no way to actually undo the damage from a harsh cleaning job. Using artificial toning to try to disguise shoddy cleaning and, especially, then selling those coins without mentioning the "treatment" they have undergone is universally regarded as deceptive and immoral.

If you ever sell them, just be sure you disclose the fact that they were cleaned and let the buyer decide.I've sold some cleaned coins on ebay and gotten near full value so not everybody thinks cleaning is a bad thing. I don't clean them and don't recommend it,but I also believe in an individual's right to like what they like.

Artificial toning is often used to heighten the value of a coin because attractive naturally toned coins bring a large premium, so many shady sellers try to pass of AT coins as naturally toned, such as with this seller:

http://cgi.ebay.com/1885-Monster-Mo...em3a61d4ed84

There are a variety of methods which include baking the coin in an oven, using chemicals, etc. As Sap said artificially toning a coin is also used to disguise any problems a coin may have.

As usual it was sort of missed that you did not say you wanted to resell them. Ever notice how many jump on a post about something with the first thing with selling a coin? Naturally if you ask about value that really makes people want to tell you about costs. However, you did ask how much, which to many means selling.
As to your #2 question. I purposely buy cleaned, washed, polished coins a real lot. Great for experimentation. Many looked like they were polished with car waxes and a dremel. After playing around here is the results:

All of these at one time looked like proofs they were polished or cleaned excessively. All went through dipps and soaks in solutions such as Laquer Thinners, Mineral Waters, Acetone, Vinegar, etc. All to get off whatever may have been put on them. All rinsed with either tap or distilled wawter at various times.
The main thing was to just put on a raw piece of wood and left on a kitchen window sill for several months. They are all still there now.
Slowly they start to look like normal coins but naturally they will always appear to be somewhat cleaned. Regardless, since I am not selling them, never will, who cares about their CLEANED VALUE?

If they were just dipped, I'd let them re-tone, but polishing is an entirely different animal. They can never be returned to uncirculated condition. But they can look like "normal circulating coins" again ...

Put 'em in your pocket with the rest of your change and carry them until they look "normal". It's what gives circulating coins that look of wear. This will remove metal and ultimately lower the grade, but if you've got polished coins, you have nothing to lose.