I put a new drive in my 13" 2010 MacBook Pro (specs in signature below) and now what it does is when I quit mail it asks me for my administrator password to re-open it.
Are you sure it's asking for your
administrator password? If so, that doesn't sound like a keychain problem.
How
exactly are you re-opening Mail? (Through an alias? Through the Dock?) Check that you're opening the correct copy of Mail, the one in /Applications/Mail.app.
If it's asking for your
keychain password, that means Mail is trying to retrieve something from a keychain that is currently locked. Entering that keychain's password will allow the data to be retrieved, but will not unlock the keychain. Each new request for information from that keychain will be mediated by a new "enter password" dialog.
Normally, all the keychain items that mail is interested in will be stored in the default keychain, the default keychain will be the login keychain (at ~/Library/Keychains/login.keychain), and it will be unlocked. You need to verify that all three of those conditions are met.
In Keychain Access, look at the list of keychains in the sidebar of the main window. There should be only one keychain named "login", it should be bold (indicating that it's the default), and it should be unlocked.
If you have multiple "login" keychains (or, for that matter, other keychains than the standard Snow Leopard complement of "login", "System", and "System Roots"), use the Edit→Keychain List menu item to get a list of all of them. ("System Roots" won't show on the list.) All of the keychains in the list should be in /Library/Keychains or ~/Library/Keychains. You can delete keychains from the list by selecting them and pressing the [-] button below the list. This removes the keychain from the list, but does not delete the keychain itself.
The problem with having extraneous keychains in the list is that when an application (say, Mail) wants an item from "the keychain", it merely asks for the item. It does not normally specify or even know which keychain the item is in. It's up to the security system to figure out which keychain, of those in the list, has the item. If that keychain is locked, it puts up an "Enter the password
for keychain ..." dialog (emphasis added). Supplying the correct password for that keychain retrieves the item, but
does not unlock the keychain. The next request to get information from that keychain produces another "Enter password" dialog. This can be frustrating if the login keychain for a different user or on a different disk volume has some info that is not also in the normal login keychain.
If your login keychain is not the default (that is, not bold), make it the default. Select it from the sidebar, and apply the menu item Edit→Make Keychain "login" Default.
If your login keychain is locked, find out why. Your login keychain is normally unlocked automatically at login, but only if its
keychain password is the same as your
login password. This is the only keychain that is ever automatically unlocked. (The OS knows the encryption keys for "System" and "System Roots" and can access them without unlocking them.) Select your (locked) login keychain, and click on the large locked padlock at the top. Verify that entering your
login password unlocks the
keychain. That will prove that the two passwords are the same.
If the passwords match, it was automatically unlocked at login but must have locked itself later. Select the login keychain and use the menu item Edit→Change Settings for Keychain "login"... to see why.