"Insufficient system resources .." Error Causes Network Problems

We have a Peer-to-Peer Network with a total of 8 PCs.  All computers are Dell OptiPlex's (620s or 280s)
and each is configured the same - 1GB Ram, 3GHz Dual Core Intel, and one 80GB Disk.  The exception is
the PC that we choose to act as a File Server (no server OS).  This PC is a Dell Precision Workstation
470 with a 3.2 GHz Dual Core Xeon processor, two 80GB Seagate disks at 15k rpm setup with a SCSI
RAID-0 controller.  All eight computers including the Xeon are running Windows XP Professional SP2 with
all being current with hardware drivers and with Windows Update run and applied to each PC with
automatic updates.

We have never had a Network problem with this setup ... until we added the eighth PC.  Our Internet
service is DSL and the DSL modem is connected to a LinkSys 8-Port Broadband Router (wired).  This is
the first time we used all 8 ports.

The Error we started to get is as follows:

"Insufficient system resources exist to complete the requested service"

This error first showed up on the New PC connected to the eighth port.  After this message appeared just
once the new PC could not perform Any functions, for example, click on "My Computer", or the START
button, or Right Click on the Desktop, anything, would cause the above error message to display.  The PC
was obviously locked and dead so a Restart had to be done and this fixed the problem (for a while).  Later
it was observed that this "Insufficient system resources .." message would appear on other PCs first then
it seemed to be infectious where up to a total of four PCs were locked up due to "Insufficient system
resources .." but it has never spread to more than 4 PCs.

I read a solution on Experts-Exchange that this error may be due to an IP allocation problem and possibly
filling up all 8 ports initiated it.  So I purchased a 16-Port NetGear Switch w/auto port sensing so that
either a Crossover or Straight-thru cable could be used from the Router to the switch.  So I connected port
four of the Router to port one on the Switch and used the ports on the Switch to connect all of the PCs.

NOTE:  The Router is configured as DHCP enabled with auto IP allocation with a range from 192.168.1.100
 to 192.168.1.155.  MTU is enabled and set at 1492.  Login as a PPPoE.

But using the NetGear Switch and only one port on the Router did not solve the problem.  We are still
suffering with the locking up of PCs due to "Insufficient system resources ...".

I think I need a "Super Guru" for help on this problem.  Please, any help will be greatly appreciated.  If
you know of a solution then please be a bit detailed so that I can follow a procedure to solve this problem.

NOTE2:  I did try and disconnect & power off one of the PC's to have only 7 PCs connected and from my
 tests of running IE and anything else on all of them not one failed with the "Insufficient system
 resources ..."  error.  I can't be 100% possitive but it seems that having more than 7 ports connected
 even with a 16-port  switch from one port on an 8-port LinkSys router causes the error to appear.

Thank you very much.