WinXP SP3 networking problem: Disconnected mapped drive

I have 2 computers a Dell D820 Latitude and a Dell Dimension 5100. both are
running WinXP SP3. I have the drives mapped for both bu for some reason
recently I have been getting this message on the laptop (Dell D820 Latitude):
"An error occurred while reconnecting R: to \\Pat-lappy\Lappy
Microsoft Windows Network: The network name cannot be found
The connection has not been restored"
This is from the laptop,

When I try to map to drives in the desktop from the laptop to access files
on the desktop (Dell 8100) I get this message:
"Attempting to connect to \\computer\drive"
Error messsage : The network path \\computer (desktop)\ drive could not be
forund."

I used to be able to access files from the laptop to the desk top and vice
versa. Now for some reason the laptop shows disconnected drives and I cannot
get the drives reconnected. Why?

Be patient with me I am know enough to be dangerous around computers at
times. There are some things I know how to do real well and other things I
do not so I may ask some "dumb questions.

Thanks, Pat