I had the very same problem last night. I'm using Internet Explorer 8. Whenever I tried to access one of my computers, it asked me to install the Remote Access Component software. After trying to install it several times without success, I contacted support. They told me that there was a conflict between LogMeIn and Internet Explorer 8 that they are currently working to resolve. (I've had Internet Explorer 8 for some time without this problem. I was told by LogMeIn that Microsoft probably patched it with a new active x control!) In the meantime, they suggested that I use the Firefox browser. I installed Firefox and found that I was able to access all my computers without any problem.
I felt the same way about installing Firefox when LogMeIn suggested it. But, since I needed immediate access to the remote computers that I access, I reluctantly bit the bullet and installed Firefox.
The installation went very smoothly and I was able to use that browser to access all of my computers. There's nothing that prevents you from using Internet Explorer 8 to access all your other websites and using Firefox only to access your remote computers through LogMeIn. (The Firefox browser is very straightforward; no learning curve necessary.) I am suggesting that you do this because there is no way of knowing how long it will take LogMeIn to sort out the problem.
Thanks for coming back and reporting your solution. It will help many others in the future. Too many people forget about the forums once their problem is solved, and that doesn't help anyone.
Once again, Thanks !!!
(DISCLAIMER: I am NOT an employee of LMI, nor do I have any financial concern in LMI. I am strictly a HAPPY USER of LMI products. I am using PC version and XP SP2. Other systems or versions may act different than described above.)