For the "clients not being able to connect" issues I would use the the OSI model...
- Check physical connectivity, are the cables properly connected, are the network cards operational?
- Check ARP table...can you see MAC adresses?
- Check IP settings, is the routing properly setup? Are people experiencing these issue able to connect on the server? (using ping, traceroute, telnet...) at this level, it can be a firewall issue as well.
- Check if packets are rejected because of errors? When doing telnet, are you able to connect but the connection is droped with error message?
- Check if you need to be connected to a VPN to access this server?
- Check if traffic is encrypted, if you need a VPN, is the VPN encrypting packets properly?
- Check for software configuration issues.
I hope I didn't screw up on the Layer/Operation match...
Obviously, if the client is able to browse or if they are already able to "use" the network, it's obviously not an issue at the first layer.
But, I did experience long troubleshooting window with lots of competent people on the line trying to fix an issue...only to realise the cable was plugged in the wrong NIC.
In a nutshell, this should be the way to troubleshoot most networking issues, that's why it's the one thing that all networking books and certifications put in the first or second chapters.