After recent Chromebook update, you may find you cannot start a reduced session of LogMeIn to access your remote machine. Because it might keep asking you the password when clicking Remote Control.
Many people encountered this problem and discussed this at the LogMeIn community.
So, how to fix this? Actually it's simple.
After you log in LogMeIn and click the link of your remote machine, you should notice the link of your remote machine as below. Please check it from the Address bar on your browser.
https://[YOUR_REMOTE_MACHINE-xxxxxxxxxx].appxx-xx.logmein.com/main.html
Just copy and change it to
https://[YOUR_REMOTE_MACHINE-xxxxxxxxxx].app00-00.logmein.com/remctrl.html?type=flash
Then you should be able to access your remote machine via LogMeIn reduced session.
Enjoy!
// 2014/1/30 Update: Great to hear it's helpful. :)
http://community.logmein.com/t5/Central/ChromeBook-can-t-login-since-last-update/td-p/106969/page/3