"The laptop can both pull and push the data. The desktop can do neither. T
issued command is:
rsync -vva --exclude=.*mozilla* --exclude=.*chromium* ~/
bmike2@192.168.0.3:/home/bmike2/;rsync
-vva --exclude=.*mozilla* --exclude=.*chromium*
bmike2@192.168.0.3:/home/bmike2/
~/"

looking at your rsync command syntax, if I understand, bmike2 is your
username on the desktop and the IP address for the desktop is 192.168.0.3.
 You have 2 rsync lines here, it appears that both are initiated from the
laptop with line 1 pushing data to the desktop and the second pulling data
from to the desktop.

"Nothing  has been added to ufw and and my router is just the modem."

If I understand you correctly you are not going through a router (level 3
device) between yourd desktop and the laptop.  in other words you have set
up a point-to-point network (level 2).  The Openssh default settings are
desigend to be used in a standard level 3 (routed environment) While it may
be possible to operate Openssh at level 2, I am not sure what changes in
ssh configuration is required to use it or when it might have issues in
point-to-point networking.

"So what do *I do*? Should I put the computers ip address in?.....
This is what I did and then I restarted the service on the desktop. But
when I tried to restart it on the laptop:"

As far as the IP Addresses I was refering makeing sure you were using the
correct addressing for the desktop and laptop - whatever the ifconfig lists
as the inet addr: is the current IP Adress assigned to that computer.

to check if openssh is installed, running, and  who is using it us the
following commands on both systems:

type this to see if it is running:  sudo netstat -anp | grep :22
This will tell you which IP Addresses are assigned to ssh tunnels

type: sudo ps -ef | grep sshd  to find out which user(s) is logged in to
ssh sessions.

Type: dpkg --get-selections | grep openssh-*  to find out if Openssh is
installed on the system. If it is you should see the following:

openssh-client              install
openssh-server             install

To install it if it isn't installed type: sudo apt-get install
openssh-server








-- 
James