Telling a network block from a refusal
A service refusing you returns a page with an explanation. A network blocking you returns nothing, a timeout, or a page from somebody else. Checking whether the page loads at all is the first and fastest test, and it decides whether the service can do anything for you.
Both end with no chat on your screen. Only one of them is a decision the service made, and only one of them can be affected by the service in any way.
Does anything load?
A refusal from a service is a page: it has the site's design and an explanation. A network block is silence, a timeout, or a notice from a filtering system that does not belong to the site. If you never saw the site's own design, the site was never reached.
Does another site behave the same way?
Try 2 unrelated sites in the same category. A network block usually covers a category rather than a single site, so if 3 chat services fail identically the block is upstream. A single service failing while others work points at the service.
Does another network behave differently?
Switching from office wireless to a phone connection is the cleanest test there is. Working on one network and not on another proves the block is in the network, and it takes 30 seconds.
What follows from each
If the service refused you, the service could in principle change it, and a service that runs no country check has nothing to change. If the network blocked you, nothing on any website can reach past it, and pages promising otherwise are describing a proxy rather than a chat.
Straight answers
Why does a block sometimes show a page?
Filtering systems in schools and offices often serve their own notice. It is a page and it is not the site's page, and the branding usually gives it away.
Can a service tell that I was blocked?
No. A request that never arrives is invisible to it, which is also why support cannot help with this case.
Is a slow connection the same as a block?
No, and it can look similar. A block fails consistently at the same point; a slow connection fails at different points each time.
Try this on a different network and compare the result.
Open unblocked chat