Three Pc Home Network Help

I'm desperately trying to get a three-pc home network / internet sharing to work. I've tried to be as comprehensive and accurate as possible in describing the problem(s).
I would be very thankful for any help.

Topology:
[cable modem]
[wireless router]
|_____[WinMe desktop]
|
|_____[XP Home laptop]
|
|---------[Win98 (not SE) laptop]

Wiring:
* The cable modem is plugged into a Netgear wireless router.
* The WinMe desktop and XP laptop are connected to the router via Ethernet cables.
* The Win98 laptop is connected to the router via a Netgear wireless adapter (wi-fi link said to be 100% OK).

IP configuration:
* The PCs are properly assigned their respective IP address by the router dhcp.
* The router IP is properly set as the default gateway.
* All three PCs can ping the router, and all three get Internet connection.
* But then:
- WinMe can ping XP, but cannot ping Win98
- XP can ping Win98, but cannot ping WinMe
- Win98 can ping XP, but cannot ping WinMe

Windows networking:
* I've tried running the Network Wizard seperately on WinMe and XP, specifying the same workgroup name;
* I've tried running on both Win98 and WinMe the NETSETUP floppy created from XP,
and I also tried to run the WinMe floppy on Win98 (it's not SE so no own Wizard; and you cannot run a non-XP network setup floppy on XP);
* BUT the network connections do not work:
- Sometimes the two other PC appear in the workgroup, sometimes just one,
- And sometimes no PC at all -- WinMe and Win98 have a tendancy to lose connection to the very own workgroup that was created on them; in XP the workgroup may still appear but the PC does not recognise itself in it!

I would reckon IP issues are the source of the Windows networking problems. But since all PCs get Internet connectivity, the router must be fine, and also the IP settings on each machine... So how come they don't 'see' each other, and not even themselves sometimes?
Also, this network *DID* work when I first set it up a couple of months ago, but since then it has been behaving randomly and now it does not work at all (apart from Internet sharing)... this is illogical, captain.

Can anyone help?