Cannot PING printers

Hi everyone, I'm not a beginner but this problem is keeping me awake at
night. I have a small Cat5 network with a Netgear FS-108 8 port fast Ethernet
switch. Attached to that I have a HP Color LaserJet 4450-HDN and a HP4000,
both with Jetdirect cards and two boxes, 1 Vista (all updated) and the other
XP, SP2 (all updates). I can PING the Vista box (and the XP box) from the XP
box but neither printer. From the Vista machine I can PING both printers (and
the Vista box) but not the XP box. Since I can print from the Vista box I
assume my setting on the printers are OK. The computers both access the
Internet without problem. The printers are shared correctly and show up as
being connected on the XP box in My Network Places, i.e. no red x’s, but if I
send a job to either printer both time out and I get the error message that
the job didn’t print, obviously since I can’t PING the printers. I tried
setting up a TCP/IP port and forcing the install with the correct IP and
driver but it still didn’t print. Temporarily I have a parallel cable to one
of the printers from the XP to be able to print and that works fine, so it’s
probably not a hardware problem. So what’s up?? Can anyone guess? –Bill