Many servers have little apps running that help protect the server from hackers/crackers that might try a dictionary type attack on a server. Think Ubuntu's most oft used/popular is Fail2Ban. If an IPAddress attempts to login X number of times and fails to provide the correct password, the IP address is blocked - and depending upon how strict one has setup Fail2Ban that could be for a few hours or a day or X length of time ... or permanent (unless someone who has access to server clears the recorded IP address that's being blocked).
The other laptop you tried from might actually appear to the server as coming from the same IP address ... the gateway IP of whatever network you are on.
Did they suggest trying to login via this:
ssh -v loginname@IPAddressofserver
The -v in front is like turning on debugging in Moodle.
When using -v in front it outputs what's going on.
Now I am using a Mac to do this, but it should be similar on a Ubuntu.
First line output by the debug should show versions:
OpenSSH_xxxx, LibreSSL xxxx
debug1: Reading configuration data /etc/ssh/ssh_config
Shows what config file it's reading
debug1: /etc/ssh/ssh_config line 21: Applying options for *
Shows what options it's applying
debug1: Connecting to FQDN [IPADDRESSOFSERVER] port XX.
debug1: Connection established.
The last two shows it did connect to server ... the lines go on in a
working connection to show the files (keys) it's looking for to use to
connect ... i.e., send to the server. Also tries different ciphers.
What's going on ... your laptop is negotiating with the server to see how
it can connect.
Eventually, one sees:
debug1: Authentications that can continue: publickey,gssapi-with-mic,password
IF your connection attempt stops at that line ... which is what you've reported ... it could be ownerships/permissions on directories/files on your laptop ... any laptop if that laptop also Ubuntu and acquired updates to it's OS.
Ubuntu laptops are just like Ubuntu servers in that they do get updates to operating system things ... and like I mentioned earlier, there has been issues this past year related to openssl thus ssh.
This is also similar to Moodle's setup of Moodle Networking.
If nothing else, the -v will give you information you could share with helpdesk and might help them provide more targeted suggestions. There really isn't one set answer to the problem.
While Google is normally your friend, if one uses:
https://www.google.com/search?q=ubuntu+ssh+Permission+denied+%28publickey%2Cgssapi-keyex%2Cgssapi-with-mic%29&ie=utf-8&oe=utf-8
you'll see there are quite a few hits .... and the resolutions to the issue aren't always the same.
And I would be cautious about trying things that one might read.
'spirit of sharing', Ken