You don't need to reinstall mail, however, I do thing you need to reset it.
This is how you do it:
Quit mail (force quit it if necessary)
Delete the following files:
~\library\Preferences\com.apple.mail.plist
~\library\Preferences\com.apple.mail.RSS.plist
Move the folder Mail from ~\Library to your Desktop
Launch mail. It will ask you to configure a new account, if it doesn't click on the Mail menu\Preferences\Accounts\(+) to add a new account and follow the on screen instructions to add an account. if you don't know how to add an account follow this tutorial:
http://grumpynet.ath.cx/tutorials/configuremailforleopard/configuremail.php
If you need help finding the settings for your ISP check out this link or call your ISP:
http://grumpynet.ath.cx/Articles/Mailservers/mailservers1.php
After doing this you should have your mail working normally again.
NOTE: if you have folders created in your computer you can recover them by copying the Mail folder you moved to the desktop earlier into ~\Library and replace what's there. The folder ~\Library\Mail contains all your email messages and attachments, you can browse it and take a look at its structure if you want, is actually pretty cool and can help you understand how you can recover messages in the future or from another computer
NOTE 2: the term ~\ means your Home Folder (the folder with the icon of a house and your user name under Places in Finder)
I hope this help you fix your problem. Please post back to let us know if this fixed your problem or if you need more help