remove all 2nd NICs in every computer & remove switch. connect all PCs to the router.
What's the reason you turn off computer browser service? Re-enable computer browser service on every computer so each PC has a computer list.
Since you only enabled computer browser on one of the computers, only that machine will keep a computer list. Once that machine is down, no other computer has a computer list for the network to work with.
only turn on the computers you need, why do you keep them running 24/7?
finally, if you can't retire XP machines, at least retire 98SE machines that are 17 years old.