|It sounds like you may have dead ports on the switch, bad cables, or bad NIC's. There's an easy way to test.|
Unplug all the machines that aren't connecting from the switch leaving only the two that are. Now move them to different ports. Do the ports light up and can you ping back and forth between the two PC's?
If yes, the issue is either the cables on the other PC's, or their NIC's.
If not, then you have bad ports and it's time to get a new switch.
Do try all ports though to ensure you know whether or not you have any bad ports.
Now, assuming all ports lit up you'll want to know if it's the cables or the PC's NIC's. The simple way to test is leave the known good cables plugged into the switch and unplug the other end from the PC. Then, plug that end into the other PC's, one at a time. If they work, then it's the cables. If the PC's don't work, then it has to be the NIC's on the PC.