What is IP address 188.8.131.52 - I'm guessing it's your router on the network? Though the IP address seems a little odd, as it's not one in the normal private ranges (I will return to this, later)? If this is your router, then it rather looks like the issue starts between your router and your ISP. Most routers have a web interface, so try pointing a browser on your network at http://184.108.40.206
and see if that loads a web page, and if so, if it's quick. If it is
quick, I suspect that the problem may not be on your internal network, but rather either on your broadband connection or at your ISP - I would contact them to check this - they can run diagnostics on your line and see if there's a problem there.
Alternatively, this could be a USB router hanging directly off your server. If this is the case, and you're running traceroute from your server, can you please also show us a traceroute from a workstation on the network - I'm guessing it will be quick to your server and then slow after that, which also implies either a problem with your broadband connection, or a problem at your ISP. In this case, one last test you may also be able to do is to check (if it is a server acting as the network gateway) to see if Apache is installed (note that it may be installed, but not running by default) on the server. If so, fire it up and see how the client machines go connecting to its
web pages (note that you may also have to open up port 80, temporarily, on the firewall to do this). Again, if it runs fine then it points to a broadband/ISP problem.
If you do go to your ISP, go armed with these screenshots of traceroutes and pings, both to your internal servers and externally, so that you can demonstrate to them that it's not a problem with your internal network (depending on how helpful they are, they may try to fob you off or assume that it's your network at fault) and where the latency starts to creep in. The more information you can give them from the start, the more competent you look and also the easier it makes it for them to know where to start looking (plus you may, if applicable, get your call escalated up from front-line support, more quickly)