About your corroded dug George Washington Inauguration button's dollar-value:
The general rule-of-thumb in the relic collecting market is, if a relic is incomplete (missing a part), OR is complete-but-damaged, OR has "significant" corrosion, its dollar-value is 50% less.
Speaking as both a longtime relic-digger and relic-dealer, I can testify that the reason for that rule-of-thumb 50% off is, most collectors would prefer to pay twice the price of a damaged-or-incomplete-or-rough specimen to get a "nice-condition" one.
For example, at a civil war relic-show, if you put a "nice-condition" Oval US buckle priced at $200 next to a "rough-condition" one at $100, you'll probably sell the nice one at that show, and you'll probably still have the cheaper-priced rough one sitting on your table three relic-shows later.
I should also mention:
Contrary to popular belief, a relic's dollar-value in NOT set by the relic dealers. In actuality, the value is set by the customers. A dealer can put whatever value he likes on the price tag -- but if the customers don't agree with his appraisal of it, that relic will still be sitting on his relic-show table (or website) a year later.
In reality, it's the customers who tell the dealers what a relic is worth, not the other way around.
You asked:
> Do you think it's worth anything in its condition?
The best way to get an accurate idea of a relic's dollar-value is to check Ebay's "Completed Transactions" statistics for that particular kind of relic (and its condition). The asking price you see on the internet means almost nothing. It's what that type of relic has "consistently" sold for that matters.