Letting the battery die shouldn't stop the password from being recognised. It has an internal battery in it for that, which wouldn't go flat in ages, if at all.
Login screen where? BIOS or in Windows? If Windows, battery has NOTHING to do with.
If it is the case, click F8 repeatedly just after it boots/beeps. It will ask you where to boot, boot in safe mode, and then log into the Administrator, and delete the user password.