Hi,

Re-check the settings for that account in Livemail.

Sometimes (Well every time) when a Hotmail account is set-up it gets the settings wrong, correct them & all should be well.

Download ccleaner. Untick any registry changes. (do not touch registry). Clean cookies, etc. Anything you are not sure of ask here. Again, untick registry, do not clean registry.
You will delete cookies, temp files etc. You should be ok.

Ask here if you do not understand what to tick.

Warning
All remembered passwords etc will be forgotten, You have to sign into them again to reset; for all accounts.

Actually no

everything the ccleaner does you can do manually
What do you want to do?

Everything that is remembered on your computer is done with cookies; passwords, IDs etc.
Follow this tutorial, clear all cookies. And then see if anything is changed.

Remember if you delete cookies, all of your accounts will lose all cookies. You will have to sign in to each one of your accounts again to set up new cookies.
Further this MAY not work.
However, cookies are a possible suspect.
Cookies - Delete - Windows 7 Forums

This will remove corrupt cookies so you can replace with new ones.

We can start with the selective option
Delete only those that have to do with messenger and the problem account.