“When the computer is switched on without *any* connection to the router”
Are you saying that even if there is no Ethernet cable connected from the router to pc you lose the connection?
“The disconnection is not instant however, the computer stays connected for approx. 20minutes, and then the connection drops”
Are computers all running XP?
Check the Lan card and network setting on all computers also the router set up
If a Vista computer Disable IPv6 In Vista
Windows Vista contains both the familiar IPv4 stack and the new IPv6 stack.
IPv6, when it's rolled out across the Internet over the next few years, will bring an end to
the problem of running out of IP addresses and improve other aspects of TCP/IP
However you do not need IPv6 at present time disable IPv6 in Vista
Download the pdf file will tell you how to disable IPv6 in Vista