Solution 1:

"...at the local library network..."

Most likely the library's firewall/router appliance blocks RDP. This is a good security measure to keep bad actors from attempting to take control of compromised PCs inside the library's public net, as well as keeping bandwidth down from users who should be using the library net for library-related activities such as database searching, etc. I bet a port scan will show other blocked protocols as well.

We lock our network down tight where I work.