OK. Lets' go back to this post:

At work for some reason, we have both PoP/SMTP and Exchange accounts set
for everyone (PoP comes before Exchange).

Initally I had only PoP configured at home, but realized that some mails
were not coming through and hence added Exchange account as well. Now to
receive mails at home, I had to check the box for "Keep a copy on server"
on
the office PCs.

This says to be that you're referencing not only an Exchange server and one
or more POP accounts at work and you are downloading those POP messages.
The normal settings for POP are to download messages from the server and
remove the messages from the server. If messages are remove from the
server, naturally, they will not be there to see if you connect to that same
mail server from some other machine. Since it appears that all the PCs at
work reference this same POP server, unless you tell them all to leave the
messages on the server, the messages will not be available for downloading
when you connect with your home machine.

You should be delivering all your messages to the Exchange server and
referencing that with an Exchange account both from home and at work. That
way all the messages will be available both from home and work and you will
need only an Exchange account at home.
--
Brian Tillman