If you have the chance to get a network card with an Intel 82558 / 82559 chip (a Pro/100 or similar), DO IT, seen so many disagreements with Realteks, on machines where the Intel based just drops in and runs. I'd take a used one of those over a brand new 8139 any day.
In Windows 98, bring up the Device manager and view resources by connection - IRQ - see where they are going.
Older PCI systems use "PIC" mode for assigning interrupts, assigning 4 spare interrupts from the ISA pool to the PCI pool, and rotating them between PCI INTA-INTD across the slots.
http://www.webopedia.com/quick_ref/IRQnumbers.asp
If the system has a typical set of devices, there may only be 3 spare, resulting in greater duplication, and while PCI devices are supposed to be ok sharing interrupts, some devices are more ok than others, so BIOS disabling an unused serial or parallel port may help by adding another available IRQ.
Clearing ESCD in BIOS is another possibility, it might reshuffle the resources better when they reconfigure, but can be a pain if you have old ISA PnP devices that need setting by Isa Configuration Utility - they will need resetting.
It's rare, but sometimes you can find an IRQ map in the documentation for the motherboard.
In addition to the PCI cards competing for those IRQs, they also include AGP and USB.
In the most dire cases, you have to deliberately put cards that can share, where they get shared, so the troublemaker gets a resource to itself - in my case I was juggling resources around a SCSI card, and had to move other cards to make sure it got an IRQ to itself.