Nobody seems to have chimed in to help. You say there’s 6 computers, most likely connected by a hub or switch. You need to do that ping from all 6 computers and compare. If all 6 have the same problem, it is most likely a switch or router problem. If you bypass the switch and plug direct into the router with a crossover cable you can eliminate the switch. Beyond that, I would watch system resources on your router (CPU Load) and see if it is high (80-100) or low (0-20) while pinging. You may have a bad cable or bad network card in your router.
Try those things, if the first test (ping from all 6) nets only 1 computer as a slow pinger, then you should check that computer specifically, and try changing the port you are plugging into on the switch. It could also be a virus on your network, that’s always something to check.