In order to use LogMeIn, the computer you are trying to access must have a password associated with it. However, not all versions of Windows require the use of a password. In the case that there is no Windows password, a hidden windows user, called LogMeInRemoteUser, will be created.
The access code you create when installing LogMeIn actually corresponds to the LogMeInRemoteUser Windows account. If you create an access code, you will not be prompted to enter the username, because the LogMeIn software detects the LogMeInRemoteUser account. If you were NOT prompted to create an access code, you should enter the Windows username and password that you use when Windows is starting up.