LogMeIn shows your Mac as Offline even though you know it is Online.
On Macs with File Vault or File Vault 2 enabled in OS X, LogMeIn is unable to go Online until you enter your password locally each time the Mac boots. File Vault / File Vault 2 is using your password to encrypt the disk; no applications can start while the disk is in this state. This problem frequently arises after a remote reboot.
Someone physically present at the computer must log in with a valid Mac username and password.
Hint: For computers in a trusted location that you regularly access via LogMeIn, you may want to consider disabling FileVault.