Unable to connect to adobe servers and open creative cloud app

James, are you using Plusnet as your Internet Service Provider?  If so, then see https://community.adobe.com/t5/download-install-discussions/plusnet-authentication-problem/m-p/13089733/page/2#M555642 which discusses how to manually update the computers network settings to reliably access Adobe servers.

if you have a recent os, your default browser must support tls 1.2, https://helpx.adobe.com/x-productkb/multi/eol-tls-support.html

to test your default browser's tls you can use , https://clienttest.ssllabs.com:8443/ssltest/viewMyClient.html

if you don't have a recent os, your computer's openssl can also be the problem.

and, i'm assuming, you've done all this:

confirm that you can connect to the secure adobe servers by reading, http://helpx.adobe.com/x-productkb/policy-pricing/activation-network-issues.html do you see both logos? if you can and still see a connection error try these steps, https://helpx.adobe.com/download-install/kb/common-network-connectivity-issues.html if those all fail, white list the adobe network endpoints, https://helpx.adobe.com/enterprise/kb/network-endpoints.html

and to contact adobe support:

using a browser that allows popups and cookies, contact adobe support by clicking here, https://helpx.adobe.com/contact.html?rghtup=autoOpen
in the chat field (lower right), type AGENT
be patient, it can take quite a while to reach a human

p.s. if you're contacted by anyone (via email or private message), it's much more likely to be a scammer than an adobe representative. ie, double check for an employee badge if contacted in the forums and look for an adobe.com domain in the email address if you click reply to an email. then check again and be very suspicious. any other method of contacting (or offering to contact you) is almost certainly a scam.

p.p.s you can also use phone (but chat is usually quicker), https://helpx.adobe.com/contact/phone.html