Can you right click on the desktop or elsewhere in Windows? If not, a check of your mouse properties in Control Panel may help.
Otherwise I have only this suggestion to offer:
A temporary work around for the IE issue would be to use the shift button on your keyboard while clicking a link. This will open the link in a new window using the left mouse button.
Take care not to hold the right hand shift button down too long as it activates Windows Sticky Keys which can be a pain to undo.
Good Luck!