Here's an update: I put the home laptop into standby before leaving.
There is a button on the laptop to turn off the network card. It's lit
up when the card is on. I noticed the light went off when the machine
was in stand by. I don't think there is any way OE can check email
and cause the locking issue since the network card is not working.
Additionally, I shut down OE before putting the laptop into stand by.

At work, I still have the locking problem. It isn't an OE specific
issue. When I try to access my email through the hosting company's
webmail interface, I get the locking error that OE gives:

Connection Failed: Can't get lock. Mailbox in use - [mydomain].com Mail
Login

Everything always works fine from home. I'm thinking this has to be
something with the setup here at work. The hosting company says it
works fine for them. I think they have given up. It does seem to be
on my end but I have no idea what it is.

Any ideas?

Thanks,
Brett