The configuration of ssh server is done in a file called /etc/ssh/sshd_config.
You should open this file and check the following:
1) Is there any of the following instructions?
If so, you will have to change it to allow connection as yourself.
2) Is there an instruction stating:
If there is, it means ssh authentication can occur only through cryptographic keys. Since you obviously do not have one, this effectively bars you from ssh'ing into the system.
Change this to
so that you may test whether this is the whole solution to your problem. Once you have persuaded yourself ssh works for you too, establish a cryptographic key for yourself, and turn off Empty Passwords again. On the Net there many useful guides on how to use keys rather than passwords for authentication. Do it. Your security will greatly improve.
To complete this test, you will have to restart your SSH server, otherwise the changes introduced into /etc/ssh/sshd_config will not come into effect. Doing that depends on your system:
sudo service ssh reload
sudo systemctl reload sshd
(the first one is for Debian and derivatives, the second one for Arch Linux, Fedora, and in general systemd systems).
If this still does not solve the problem, you will have to povide debugging details, which can be obtained by issuing on the client machine
ssh me@my_pc -vv
which output a fair amount of data, useful for this task. There is an equivalent option to be issued on the server: you need first to stop the service,
sudo service ssh stop
sudo systemctl stop sshd
and then restart it with
sudo /usr/sbin/sshd -Dd
sudo /usr/bin/sshd -Dd
again for the to types of systems (I am not sure for systemd distros apart from Arch, perhaps the first form applies to all systems apart from Arch).
This will generate info necessary for debugging.