Yahoo, like any service depends on membership data (accounts) to sell their product to merchants, so I have never heard of anyone EVER deleting members because of inactivity or other reasons except unlawful or similar reasons. Every user is more money they can charge for services, and they surely are not looking for the CREAM of the CROP members, just head counts.
I'd wait the 48 or longer hours, and if anything happened THEN I'd contact Yahoo - otherwise, I'd chalk it up to just another hair-brained semi-plausible scheme to rob account info by dirtbags. My thinking, what is the worse that will happen if it is real vs. what is the worse to happen if it is a scam and there is no comparing and I'd always err on caution's side.
This sounds like a scam from the first word - why would Yahoo need YOUR username or password 1)without your user-name, they couldn't contact you, 2) if you lost your password they would email or reset it, or however it is done according to their practice.
This sort of email I have seen with very convincing logos from Ebay, Paypal and others, mainly because scammers (with very legitimate URLs) just copy and past the logos onto their pages.
Giving user/pass to anyone lets them have access to all your account.email and they search for any private data through correspondence. I would not reply to any mail from anyone I get services through, they know who I am and they know how active I am, surely they are the LAST PEOPLE to ever need my info.