I received new messages in my email program at home, but there were no emails in my account when I checked it through Web Mail later on. Why can't I get those emails in Web Mail?
When you have already download your emails through your email program, usually those emails will be deleted from the server. This means that you will not be able to download them again from another location or from your Web Mail program.
If you check the setting for "Leave Mail on Server" in your email program, you should be able to download the same emails through Web Mail and your email program.